# Firmsconsulting

## Financing transactions with stock swaps

In Corporate restructuring, Finance, MBA on October 27, 2010 at 8:13 pm

Stock swap transactions are one of the popular ways in which mergers can be financed. It refers to the situation when an acquiring company exchanges its common stock shares for common stock shares of the target company at the agreed upon ratio.

The ratio, which is called ratio of exchange, is determined during merger negotiations. The acquiring company often needs to repurchase shares in the market place to obtain an adequate amount of shares to be able to complete the transaction.

To find the ratio of exchange, the dollar amount required to be paid per share of the target company must be divided by the market value of the shares of the acquiring company.

Test yourself:

ABC Company would like to acquire company BCD by using a stock swap transaction to finance the merger. ABC’s shares currently trade for \$60 per share. BCD’s shares are traded for \$55. However, in merger negotiations, it was agreed that BCD’s shares should be valued at \$90 per share. What is the ratio of exchange in this merger transaction?

Solution:

The ratio of exchange is 1.5 (90/60). ABC will need to exchange 1.5 shares of common stock to obtain 1 common stock share of BCD.

Test yourself:

ABC (acquiring company) is acquiring BCD (target company) with the use of a stock swap transaction where it will exchange 1.5 shares of common stock for each common stock share of BCD. ABC’s shares trade at \$60 per share. It was agreed during merger negotiations that BCD’s shares will be valued at \$90 each. The real market price of BCD’s shares is \$55 per share. Find out how many shares does ABC need to exchange in the stock swap transaction if BCD needs to obtain 15,000 shares?

Solution:

ABC needs 22,500 (15,000*1.5) to complete stock swap transaction with BCD at a ratio of exchange of 1.5:1.

Test yourself:

ABC (acquiring company) is acquiring BCD (Target Company) with the use of a stock swap transaction. ABC’s earnings before the merger were \$400,000 per year and it has 110,000 of shares of common stock outstanding. ABC will have to issue 22,500 shares of additional common stock to complete the stock swap transaction with BCD. BCD’s earnings before the merger is \$65,000 and it has 15,000 shares of common stock outstanding. The ratio of exchange is 1.5 of ABC’s shares for 1 share of BCD.

What are current earnings per share (EPS) of ABC and BCD and what will be the initial earnings per share of ABC after the merger, if earnings are assumed to stay unchanged?

Solution:

Current, (before the merger) earnings per share (EPS) of ABC is \$3.6 (400,000/110,000).

Current, (before the merger) earnings per share (EPS) of BCD is \$4.3 (65,000/15,000).

Initial earnings per share of ABC after the merger are:

= ((400,000+65,000)/(110,000+22,500))

=485,000/132,500

= \$3.5

It is common for earnings per share of acquiring company to initially decrease. This happens because acquiring company pays a large premium above the target company’s market price. In the long run, however, earning per share will likely be higher than it would be without the merger.

If the price/earnings ratio (P/E ratio) paid for the target firm by the acquiring firm is greater than the P/E of acquiring firm then, the EPS of the acquiring firm will initially decrease and vice versa. However, in the long term, the EPS of acquiring firm should increase. The P/E Ratio is found by dividing the market price per share by earnings per share (EPS).

Test yourself:

ABC (acquiring company) is acquiring BCD (Target Company) with the use of a stock swap transaction. ABC’s market price is \$60 and its earnings per share are \$3.6. BCD’s market price is \$55 and its earnings per share are \$4.3. However, during merger negotiations ABC agreed to a 1.5 ratio of exchange where it value BCD’s shares at \$90.

A. Explain how ratio of exchange was determined.

B. Calculate the P/E ratio for ABC and BCD before the merger at market prices per share.

C. Calculate the P/E ratio of BCD at the agreed upon price per share for the merger.

Solution:

A.

The ratio of exchange of 1.5 is calculated by dividing \$90 (the agreed upon price of BCD’s share) by \$60 (the market price of ABC’s share). ABC will need to exchange 1.5 shares of common stock to obtain 1 common stock share of BCD.

B.

P/E ratio of ABC before the merger is \$60/\$3.6=16.6

P/E ratio of BCD before the merger is \$55/\$4.3=12.7

C.

The P/E ratio of BCD at the agreed upon price per share for the merger is:

\$90/\$4.3=20.9

The P/E ratio paid by ABC for target company (BCD) was larger than the P/E ratio of ABC. This was due to an agreed upon price for BCD common stock shares which was \$35 (\$90-55) or 63.6% (35/(55/100)) above the  target company’s market price. It is common for an acquiring firm to pay approximately 50% above the target company’s market price. Consequently, in such situations the P/E ratio paid is often higher than the acquirers P/E ratio. This results in the initial earnings per share to be lower after the merger.

## Establishing a value for the target company

In Corporate restructuring, Finance, MBA on October 27, 2010 at 8:11 pm

An acquiring company may be interested in acquiring entire businesses or just acquiring individual assets and selling off the rest of the assets. When considering a merger, companies can use capital budgeting techniques to find the value of the company. If the net present value of the relevant cash flows is positive then a merger is considered acceptable.

If the acquiring company is interested in the whole business rather than in just few assets of the target company then post-merger pro forma statements for the target company should be prepared and the cost of capital of the acquiring company must be adjusted to reflect the cost of capital of the target company.

Test yourself:

ABC Company would like to obtain the assets of BCD Company. BCD Company is a loss maker, it made losses over the last 4 years. However, it has three assets which ABC needs for its operations which are assets a, b and c. BCD is not willing to sell the assets separately but willing to sell the entire company for \$95,000. According to the balance sheet of BCD;

• asset a is worth \$25,000,
• asset b worth \$20,000
• And asset c worth \$50,000.
• BCD also has \$5,000 in cash,
• ABC found out that they can sell accounts receivable and inventory of BCD for \$10,000, and
• BCD’s liabilities account for \$70,000.
• Taking into account merger tax advantages from losses, after the merger, three assets of BCD will generate \$15,000 in cash inflows over the next 10 years.
• ABC’s cost of capital is 12%.

How should ABC establish if it should undertake this investment?

Solution:

BCD requires \$95,000. Out of this money, \$70,000 will be used to cover liabilities and \$25,000 will be going to the owners of the target company. ABC will be able to recover \$10,000 from selling accounts receivable and inventory and it will also obtain \$5,000 in cash. Therefore, its actual investment is \$80,000 (\$95,000-10,000-5,000).

Next we need to determine the net present value of the relevant cash flows. Since it is an annuity, we can calculate it very simply. We will use a financial calculator. The calculation is as follows:

PMT: 15,000

N: 10

I: 12

PV: calculate = 84,753

Since investment required is \$80,000, we can find the NPV as follows:

84,753 – 80,000 = 4,753

There is another way to calculate NPV using a financial calculator. It is advisable to try them both to make sure that the answer you obtain is correct. The second way is as follows:

CF0: -80,000

CF1: 15,000

Second function Nj: 10

I: 10

Second function NPV: calculate = \$4,753

Since both calculations gave us the same answer, we can be confident that the answer is correct.

Since NPV is \$4,753 which is higher than zero, a merger with BCD is acceptable.

## Financial (Capital) Lease

In Finance, Leasing, MBA on October 27, 2010 at 8:01 pm

Finance or financial (capital) lease refers to the lease of the asset where the useful life is closely aligned to the term of the lease. The lease term is longer than operating lease. Finance leases are usually leases for an asset which does not become technologically obsolete. Under a capital lease, the lessee is usually responsible for all maintenance and other costs. Comparatively, under an operational lease, lessor is usually responsible for such costs.

A lessor purchases an asset selected by the lessee. The lessee will be able to use the asset during the duration of the lease agreement as long as contractual, periodic and timely payments are made by lessee to the lessor.

At the end of the term, the lessee may have a purchase option which allows the lessee to acquire an ownership of the asset. The lessee is not allowed to cancel the lease which makes a financial lease similar to long-term debt. If a lessee misses contractual or periodic payments, the lessee may be forced into bankruptcy.

Because under a finance lease, the lessee may have some ownership of the asset with some risks and benefits that comes with ownership, a finance lease must be recorded as a capitalized lease. This refers to recording the present value of all contractual payments and assets and corresponding liabilities on the balance sheet.

Under a finance lease, the firm benefits from the tax-deductibility of the interest paid on the leased asset as well as from depreciation of the leased asset which is recorded as an expense on the firm’s income statement.

This leads to increases in the debt/equity ratio and therefore an increase in financial leverage compared to an operational lease. It also leads to a decrease in working capital due to an increase in current liabilities.

Moreover, part of the payments due to a financial lease are recorded as a reduction in lease liability under operating cash flows and part is recorded as lease interest payments under financing cash flow. This leads to an increase in operating cash flow compared to records under operating lease where only operating cash flow is affected.

Because firms have an incentive to report leases as operational leases, certain regulatory rules were established by Financial Accounting Standards Board (FASB) which specify which assets can qualify for operational leases. The following is a list of characteristics. If even one of such characteristic is met than an asset should be recorded as financial lease.

• A lease term is 75% or more of the useable life of the asset.
• At the commencement of the lease agreement, the present value of the lease payments is equal to 90% or more of the fair market value of the leased asset.
• Ownership of the asset is transferred to the lessee at the maturity of the lease agreement.
• A lease agreement contains an option to purchase the asset at the “bargain price” which must be the fair market value.

## Dividend policies

In Dividends, Finance, MBA on October 27, 2010 at 7:53 pm

An important concept to know when it comes to the distribution of dividends is the dividend payout ratio. The Dividend payout ratio indicates which percentage of each dollar earned is distributed in cash to the shareholders. It is calculated as follows:

Dividend payout ratio = cash dividend per share/earnings per share

Generally the higher the dividend payout ratios the more attractively are shares of the firm seen by investors. Dividend payout ratios vary significantly between industries and organizations. The liquidity position of the company is one of the factors that affect the dividend payout ratio the company selects.

Test yourself:

ABC Company issued cash dividends of \$3 per share. ABC’s earnings per share are \$8. What is the dividend payout ratio?

Solution:

Dividend payout ratio of ABC = 3/8 = 37.5%

This indicates that out of each dollar of earnings, 37.5% is distributed to shareholders as cash dividends.

Constant payout ratio dividend policy – according to this dividend policy, stockholders receive dividends at a fixed percentage rate from earnings every financial period that resulted in a profit. In financial periods when loss is incurred, no dividends are distributed. Dividends increase or decrease based on the amount of profit the firm made during a particular year. This type of dividend policy is not recommended because fluctuations in the dividends from one period to another may adversely affect the share price.

Constant dollar (stable) dividend policy – according to this dividend policy, a fixed amount of dollars per share are paid each period which resulted in a profit. The amount of fixed dollar dividend only increases after an increase in earnings proves to be stable.

Regular with extras dividend policy – according to this dividend policy, fixed amount of dollars per share is paid every period. On years when the profit exceeds normal, extra dividend is paid.

Residual dividend policy – This dividend policy is aligned with the residual theory of dividends. The residual from retained earnings is paid after all acceptable investments were undertaken.

Target dividend payout ratio

It is advisable for firms to establish target dividend payout ratio and then use it for guidance in determining dividend levels. Target dividend payout ratio refers to a specific percentage of earnings that firms would like to pay in dividends.

For example, if the target dividend payout ratio is 40% then the firm intends to try to keep its dividends around 40% of its earnings. The Target dividend payout ratio is very useful in cases of constant dollar dividend policy and regular with extras dividend policy. Under these policies a regular dividend is paid each period. However, organizations can use the target dividend payout ratio as a guide to decide when dividends can be adjusted to reflect a stable new level of earnings.

Shareholders usually prefer regular and regular with extras dividend policies because in involves a smaller degree of uncertainty regarding the dividends to be received in each period.

Cash dividends and stock dividends

Cash dividends are dividends which are paid out in cash to the shareholders via cheque or electronic transfer. When cash dividends are distributed to shareholders, the share price tends to drop by an amount similar to the cash dividend. This occurs because the economic value was distributed from the firm to shareholders. Shareholders have to pay tax on cash dividends. Therefore, the amount that they receive decreases in value.

Stock dividends are dividends paid out in additional stock. There is no cash outflow. The funds are just shifted between accounts (from retained earnings to common stock and paid-in capital in excess of par). If a company issues a 3% stock dividend this means that if one owns 100 shares of this company than 3 additional shares will be received. Overall, stock dividends do not bring any value to the shareholder. Stock dividends decrease the share price.

To determine by how much share the price will decrease, let’s look at an example. Assume that shares of ABC sold for \$17 each. ABC decided to distribute a 10% stock dividend. The share price will decrease as follows: \$17 * (1/1.1)=\$15.45.

If individual Y owned 1,000 shares before the stock distribution, after stock distribution individual Y will own 1,100 shares. The market value of shares of individual Y remains unchanged as shown below:

1,000 * \$17     = \$17,000

1,100 * \$15.45 = \$16995

Therefore, as can be seen from the above, the shareholders’ market value of shares remains unchanged.

If the most recent earnings of ABC were \$350,000 and individual Y owned 1% of the firm’s shares than earnings per share before stock dividends were \$3.5 (\$350,000/\$100,000). If earnings are expected to stay the same than after the stock dividends, then earnings per share would decrease to \$3.18 (\$350,000/\$110,000). Individual Y’s share in earnings stays the same. It was \$3,500 (3.5*1000) and now it is \$3498 (3.18*1,100).

Shareholders do not really obtain real value due to such stock dividends. It is more a perceived value of obtaining more stock. Consequently, shareholders generally do not have to pay tax on stock dividends unless the cash dividend option is present. For organizations, stock dividends are more costly but can be appropriate if the organization needs cash to finance a rapid growth.

Test yourself:

ABC shares are currently sold for \$20 each. ABC decided to distribute 5% stock dividend. By how much the share price will decrease?

Solution:

The share price will decrease as follows: \$20 * (1/1.05)=\$19.05.

## Establishing a dividend policy

In Dividends, Finance, MBA on October 27, 2010 at 7:51 pm

Dividend policy refers to the policy which is used as a guide when a firm makes dividend decisions. It assists the board of directors in establishing how much should be paid to shareholders in dividends.

Dividend policy should be established in such a way that it provides for adequate financing for the firm. Dividend policy must also be aligned with the main objective of the firm which is to maximize shareholders’ wealth.

Investors tend to prefer stable increasing dividends as opposed to fluctuating dividends.

Factors which affect dividend policy

There are number of external and internal factors which affect dividend policy.

External factors which affect dividend policy

Contractual constraints – refer to restrictive provisions in a loan agreement and may include dollar or percentage of earnings limit on dividends and an inability to make dividend payments until certain levels of earnings is reached.

Legal constraints - this type of constraints depends on the location of the firm. Usually, due to legal constraints, firms are not able to pay out any dividends if the firm has any overdue liabilities or if it is bankrupt.

Firm also cannot pay any part of par value of common stock. Sometimes, in addition to the inability to pay any part of par value of common stock, firm also may not pay any part of paid-in capital in excess of par.

Market reactions – a firm needs to consider how markets will react to its dividend decisions. For example, if dividends are not paid or decreasing then markets will see it as a negative signal and the stock price will likely to drop. This will decrease shareholders’ wealth. If dividends are paid out consistently or even increasing in amounts, this can be seen as a positive signal by the market participants and stock price will likely to increase. This will increase shareholders’ wealth.

Shareholders generally prefer fixed or increasing dividends. This decreases uncertainty and investors are likely to use lower rate at which earnings will be discounted. This will lead to an appreciation of share and an increase in shareholders’ wealth.

Current and expected state of the economy – If state of the economy is uncertain or heading downward than it may be wise for management to pay smaller or no dividends to prepare a safety reserve for the company which can help to deal with future negative economic conditions.

However, if the economy is growing very fast then the firm may have more acceptable investments to take advantage of. It can be best not to distribute dividends but rather use these funds for investments.

Changes in government policies and state of the industry must also be taken into account.

Internal factors which affect dividend policy

Financing needs of the firm – Mature firms usually have better access to external financing. Therefore, they are more likely to pay out a large portion of earnings in dividends. If a company is young and rapidly growing than it will likely be unable to pay a large portion of earnings in dividends as it will require retained earnings to finance acceptable projects and its access to external financing is likely to be limited.

Preference of the shareholders – a firm should consider the needs and interests of the majority of its shareholders when making dividend decisions. For example, if shareholders will be able to earn higher returns by investing individually then what firm can earn by reinvesting funds than a higher dividend payment should be considered.

If the firm will have to issue more stock to be able to pay out dividends than it may be in the best interest of the current stakeholders not to issue dividends to avoid potential dilution of ownership. Dilution of ownership occurs because after issuing of additional stock, retained earnings will have to be distributed over a larger amount of the shareholders. This leads to dilution of earnings for existing shareholders. This also leads to dilution of control.

Firms also need to consider the wealth level of the majority of its shareholders. If the majority of shareholders are lower income earners than they likely will need dividend income and will prefer payment of dividends. However, if the majority of shareholders are high income earners then they will likely to prefer appreciation of share as it will defer tax payment even if the tax applicable on dividends and capital gains is the same, as in US after 2003 Tax Act.

Interestingly, in an efficient market, preferences of the shareholders should be met by price mechanism. If dividend payments are lower than required by many investors than those investors will sell their shares. Share prices will drop and this will raise an investors’ expected return. Higher expected return will increase the weighted marginal cost of capital and intersection between IOS and WMCC schedules will occur at a lower optimal capital budget point. Due to higher WMCC, less of the projects will be acceptable and more of the retained earnings can be paid out as dividends. Therefore the owners’ preferences are satisfied by price mechanism.

Stability of earnings – If earnings of the company are not stable from period to period than it is wise to follow conservative payments of dividends.

Earnings requirement – this constraint is imposed by the firm. It consists of a firm not being able to pay out in dividends more than the sum of the current and the most recent past retained earnings. However, the firm still can pay out dividends even if it incurred losses in the current financial period.

One of the reasons firms may want to pay dividends in years when the firm incurred a loss is to send positive signal to the market indicating that the loss is only a temporary phenomenon and that the company has its operations under control. Otherwise, shareholders may start selling shares which will decrease price of the shares and even further decrease wealth of the owners of the company (shareholders).

Lack of adequate cash and cash equivalents – occurs when firm do not have adequate cash and cash equivalents, such as marketable securities, to make dividend payments. Borrowing with intention to use funds to pay out dividends is usually not welcomed by lenders because the use of funds is not aligned with activity that would help firm to pay back debt to the lender. Borrowing to pay dividends is also usually not a wise business decision.

## Importance of dividends and dividend policy

In Dividends, Finance, MBA on October 27, 2010 at 7:43 pm

Dividends are payments made by an organization to its shareholders from earnings generated in current or previous periods. Shareholders earn income from two sources, the capital gain due to appreciation of share and dividend yield. Dividend yield is calculated by dividing the current dividend by the price of a share.

Test yourself:

You purchased shares of ABC Company for \$50 per share. Two months after the purchase of shares you received a dividend on \$3 per share. What is the dividend yield on the ABC shares?

Solution:

The dividend yield = 3/50=6%.

The stock value is determined based on the present value of all expected dividends to be received from share over the infinite future period that firm is expected to be operational. Expected cash dividends give an indication of the firm’s current and future performance.

The constant growth valuation model can be used to evaluate the expected growth of a share price. The formula for the constant growth valuation model (Gordon model) is as follows: Po=D1/r-g. As can be seen from this formula, if dividends do not grow then the share price will stay the same as long as required return stays the same. Assuming that required return is constant, for a share price to grow the dividends need to grow as well.

Test yourself:

ABC’s dividends over last few years were as follows:

2010: \$3

2009: 2.9

2008: 2.4

2007: 2.3

2006: 2.1

2005: 2

The required return is 12%. What is the price of the share? What would be the price of the share if growth of the dividends were zero and the next period’s dividend would be \$3.25?

Solution:

First we need to find the growth rate with the help of a financial calculator. The calculation is

PV: -2

FV: 3

N: 5

I: calculate = 8.45%

The ABC’s share price is found with the help of the Gordon model Po=D1/r-g:

Po=3*(1+.0845)/.12-.0845

Po=3.25/.0355

Po=\$91.65

To find the share price if the growth of dividends were zero we would use the formula Po=D1/r (for zero growth valuation model)

Po=3.25/.12

Po=\$27.08

Without growth in dividends, ABC’s share price is valued to be significantly lower.

Dividend policy is less important than capital budgeting and capital structure decisions. However, generally, dividend policies are expected to influence the price of shares.

Cash dividends are paid out of the retained earnings. Retained earnings are an internal source of financing. Therefore, if a business requires financing then the bigger the cash dividends, the higher the amount of external financing will be required. External financing can be in the form of debt or equity.

## Overview of the balance sheet – financial position statement

In Entrepreneurship, MBA on October 27, 2010 at 7:07 pm

A balance sheet – financial position statement is one of the most important financial statements. Other important financial statements include the income statement, cash flow statement and statement of changes in equity.

A balance sheet the financial position of the company at a given point in time. It is often called a “snapshot” of the company’s financial position.

### How to think about a balance sheet – financial position statement

A good way to compare the balance sheet statement, income statement and cash-flow statement is to think of a river leading to a dam. The income statement and a cash-flow statement record the movement of money over a specific period of time. It is similar to recording the volume flowing down a river over a specific period. The balance sheet – financial position statement is the dam. Everything collects there.

Therefore, by looking at the balance sheet we can see how everything comes together at a given point in time. If the company is reporting strong cash-flow in the statement of cash-flows, then that cash must be collecting somewhere, in the balance sheet. Provided a balance sheet is constructed honestly and correctly, it is a wonderful source of information about the company. Like a dam, any poisonous material or waste, gets washed down into the balance sheet. Therefore, paying careful attention to the balance sheet – financial position statement allows to evaluate important information about the company.

### Understanding the balance sheet – financial position statement

To understand the balance sheet – financial position statement, one first needs to understand the difference between assets and liabilities. A simple explanation is as follows: if you take an unpaid vacation or are between jobs for a while, assets will or will have the potential of adding money to your bank account every month. Liabilities, however, will deduct money from your bank account every month.

For example, if you own a fully paid-off house, which is currently empty, this is an asset. You may choose to earn money from this asset by renting it out. Therefore, even if you are not working, you will have rental income generated from your asset. However, if you leased an expensive car and lost your job, the bank will still deduct money from your bank account every month. Therefore, this is a liability. Alternatively, if the car is fully paid-off, it could be an asset if you could generate income from it.

We also can define assets and liabilities more formally.

ASSETS

Assets are any tangible or intangible economic resources that a company or individual possesses and which can be used to cover the individual’s or company’s debt. For example, in the case of an individual, retirement savings and stocks are examples of assets. In the case of a company, fully owned equipment and buildings are examples of assets.

As represented on the balance sheet – financial position statement, current assets are assets which are excepted to be converted into cash within 12 months and non-current assets are assets which are expected to be converted into cash at some point in the future which is longer than 12 months.

LIABILITIES

Liability is a legal obligation to settle debt which arises as a result of a past transaction or event. A liability should, by law, be settled at a specified future period or over a specified period and, possibly, at specified intervals.

As represented on the balance sheet – financial position statement, current liabilities are debts which must be settled within 12 months and non-current liabilities are debts which must be settled at some point in the future which is longer than 12 months.

An example of personal liability can be a personal loan that must be repaid to the bank. Company liability examples include accrued expenses such as wages as well as long-term loans.

## Annualized Net Present Value (ANPV)

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:37 pm

The annualized Net Present Value (ANPV) technique is the best method to use when comparing mutually exclusive projects which have unequal duration. ANPV is the most efficient technique to convert Net Present Values (NPVs) of projects with unequal duration into an ANPV for each specific project, which can then be compared.

To find ANPV, the following calculation must be made:

1 – Find NPVs for each project

2 – Divide the NPV of each project by PVIFAr,n (Present Value Interest Factor for Annuity) at the project’s required cost of capital and number of periods. The amount for PVIFAr,n can be found in financial tables.

3 – The project with the higher Annualized Net Present Value (ANPV) is preferred.

Alternatively, ANPV can be found by using a financial calculator , as shown below:

PV = use NPV

N = Number of periods over the duration of the project (e.g. number of years)

I = required cost of capital (e.g. 10%)

Find PMT = this will be the annualized net present value (ANPV)

### Test yourself

ABC Corporation has two mutually exclusive projects A and B that it can invest in. Initial investments investments required for project A and B are \$150,000 and \$200,000 respectively. The duration of project A is 4 years and of project B is 3 years. Expected annual cash inflows from project A are \$40,000 and from project B is \$70,000. The terminal cash flows from projects A and B are \$21,000 and \$34,000 respectively. The cost of capital of ABC Corporation is 9% and both projects have an average risk, which means that alteration for risk adjusted discount rate is not required. The 9% for cost of capital should be used for both projects.

What is the ANPV for projects A and B?

SOLUTION:

By using a financial calculator, we can find the solution to this problem. First we need to establish the net present value (NPVs) for projects A and B.

Clear calculator: second function, “C ALL”

CFo: -150,000

CF1: 40,000

CF2: 40,000

CF3: 40,000

CF4: 61,000 (40,000 + 21,000)

I: 9

Second function, NPV: 5,534.28

NET PRESENT VALUE (NPV) FOR PROJECT B:

Clear calculator: second function, “C ALL”

CFo: -200,000

CF1: 70,000

CF2: 70,000

CF3: 104,000 (70,000 + 34,000)

I: 9

Second function, NPV: 3,444.86

However, because the projects have different duration, we need to convert Net Present Values (NPVs) found above into ANPV for each project.

CONVERTING NPV TO ANPV FOR PROJECT A:

Clear calculator: second function, C ALL

PV: – 5,534.28

N: 4

I: 9

Find PMT: \$1,708.26

CONVERTING NPV TO ANPV FOR PROJECT B:

Clear calculator: second function, C ALL

PV: – 3,444.86

N: 3

I: 9

Find PMT: \$1,360.91

Since the ANPV of project A (\$1,708.26) is higher than that of project B (\$1,360.91), project A should be selected.

## Using a financial calculator

In Capital Budgeting, Finance on October 27, 2010 at 6:25 pm

Using a financial calculator is a skill, similar to typing. You just need to know which steps to take and then you need to practice to the point when you feel comfortable with using a calculator.

In all explanations with a financial calculator we will be using a HP 10bll. Other financial calculators are similar, yet we find it easier to work with the HP. Most text books use HP calculators when providing guidance on using a financial calculator, so if you have a different calculator you may need to spend more time learning slightly different calculation steps. Before investing further time, it may be wise to get a universally used calculator.

Before using a financial calculator to make specific calculations such as calculating NPV or IRR, it is important to make sure that you:

1 – Clear the calculator – by pressing second function followed by “C All”

2 – Set calculator for the “END” by pressing second function followed by “BEG/END” and ensuring that the word “BEGIN” is not displayed. Exceptions to this rule occur when it is specifically stated in the problem that cash flows occur at the beginning of the period (for example, at the beginning of the year).

Again, if no sign appears on the display then you do not need to reset it as it is set for “END” by default. If it says “BEGIN” on the display, you need to press second function followed by “beg/end.”

When you set the calculator for the “END” of the period you do that because in the problem you are working with, cash inflow or outflow occurs at the end of the period. If the problem does not state when cash flows occur, you need to assume that it occurs at the “END” of the period.

The majority of calculations will require the “END” setting. If it is by mistake set for “BEGIN” but cash flows occur at the end of the period, then incorrect answers will be generated.

Therefore, it is advisable to keep it set for the “END” at all times as a default and only reset it for “BEGIN” when a calculation requires that to be done. Right after a calculation is completed that requires the “BEGIN” setting, it is important to develop a habit to reset it to the “END”.

In the explanations using a financial calculator, for convenience and clarity purposes, we will generally display explanations of calculations as presented in the example below:

PV: -900 I: 7 N: 5 FV: 1,262.3

When using a HP 10bll financial calculator, or using any financial calculator, you need to first insert the number (number, e.g. -900) and then insert the purpose of the number(e.g. PV).

For example, as per above, you need to press:

900 followed by the minus sign followed by PV

7 followed by I

5 followed by N

Than press FV, and the calculator will display the correct answer

Financial calculators sometimes give false answers. It is advisable to check each calculation 3-4 times to make sure that the same answer is given consistently.

Throughout the site, if you ever struggle with a calculation, always come back to this page for some simple tips on using a financial calculator.

### Test yourself

ABC Corporation plans to invest in project C which has an initial investmentof \$500,000. ABC’s cost of capital is 8%. The operating cash flows to be generated from the project will be as follows:

End of 1st year: \$100,000 End of 2nd year: \$300,000 End of 3rd year \$250,000

1 – What is the Profitability Index (PI) for project C?

2 – What is the NPV for project C?

3 – Taking the NPV found in the previous step into account, is the project acceptable according to the NPV technique?

4 – Based on the Profitability Index (PI), is project C acceptable?

SOLUTION:

1 – First we need to find present values of the mixed stream of operating cash inflows. Using a financial calculator, we need to take the following steps:

End of 1st year:

FV: \$100,000

N: 1

I: 10

Calculate PV: \$90,909.09

End of 2nd year:

FV: \$300,000 N: 2

I: 10

Calculate PV: \$247,933.88

End of 3rd year:

FV: \$250,000

N: 3

I: 10

Calculate PV: \$187,828.7

Next we need to add up all present values from operating cash inflows to obtain the total PV of operating cash inflows:

= \$90,909.09 + \$247,933.88 + \$187,828.7

Total PV of operating cash inflows = \$526,671.67

Next we will follow the equation for Profitability Index (PI):

PI = Total present value of cash inflows/Initial investment

PI=\$526,671.67/\$500,000

PI=1.05

Therefore, the profitability index (PI) for project C is 1.05.

2 – To find NPV, we follow the formula for NPV:

NPV=Present value of cash inflows – Initial investment

Therefore, NPV for project C = \$526,671.67 – \$500,000

NPV for project C = \$26,671.67

3 – Since NPV is more than zero (\$26,671.67), project C is acceptable according to NPV technique.

4 – Since Profitability Index (PI) is greater than 1 (1.05), the project may be considered to be acceptable.

## Net Present Value Method

In Capital Budgeting, Finance, MBA on October 27, 2010 at 5:58 pm

Sophisticated capital budgeting techniques include Net present value method (NPV), internal rate of return (IRR), Profitability index (PI) and Equivalent annual annuity (EAA). NPV and IRR are discussed below.

### NPV

NPV is a sophisticated capital budgeting technique. Theoretically, Net Present Value (NPV) is the best technique out of sophisticated capital budgeting techniques but it is difficult to use it in practice. Sometimes Net Present Value method is referred to as the “gold standard” for investment decisions.

It is very easy to use Net Present Value with the help of a financial calculator if all necessary data is available. However, it is important to firstly understand the logic behind this calculation. NPV is determined by finding present value of cash inflows and then subtracting an initial investment.

NPV=Present value of cash inflows – initial investment Now, after we understand the logic behind usage of Net Present Value method, we can calculate NPV using a financial calculator. We will always use a HP 10bll financial calculator throughout the website. Other calculators are similar but may have some small differences.

Before you make any calculations, make sure that you:

1 – Clear the calculator – by pressing the second function followed by “C All”

2 – Ensure that it is set for end if cash flows occur at the end of the period and that it is set for beginning if cash flows occur at the beginning of the period.

To set for end/beginning – press second function followed by beg/end. If it is set for the beginning than word “begin” will be displayed. If it is set for the end than no word will be displayed.

Majority of calculations will be with the “end” setting (used when cash flows occur at the end of the period). Therefore, it is important to acquire a habit of re-setting your calculator to the “end” setting after every calculation with the “begin” setting. Otherwise, you are running a risk of forgetting to re-set the calculator and obtaining an incorrect result from future calculations.

NPV FOR ANNUITY IS CALCULATED AS FOLLOWS:

Initial investment: amount, minus sign, CFi

Annual cash inflow: amount, CFi1

Number of periods: number of periods, second function, Ni

Cost of capital: number, i

Find NPV: second function, NPV

NPV FOR A MIXED STREAM IS CALCULATED AS FOLLOWS:

Initial investment: amount, minus sign, CFi

Put in amount for each cash inflow separately following with CFi1, CFi2 etc

Cost of capital: number, i

Find NPV: second function, NPV

If NPV is higher than zero than we know that this project will earn returns higher than the business’s cost of capital. Further, the owner’s wealth will increase by the amount equal to NPV.

### Test yourself

ABC Corporation has an option to invest in projects A. Project A has aninitial investment of \$15,000, and operating cash inflows of \$3,000 over the economic life of the project, which is 8 years. The cost of capital (also called discount rate or rate of return) is 8%.

Find the net present value (NPV) of project A?

SOLUTION:

With the use of a financial calculator , we can find the net present value (NPV) as follows:

Clear the calculator by pressing second function followed by “C ALL”.

Make sure calculator is set to the “end”. This setting is used because in this problem cash flows occur at the end of each period. It is commonly accepted that if problem does not state when cash flows occur, you need to assume that cash flows occur at the end of the period, not at the beginning of the period.

WE KNOW THAT NPV FOR AN ANNUITY IS CALCULATED AS FOLLOWS:

Initial investment: amount, minus sign, CFi

Annual cash inflow: amount, CFi1

Number of periods: number of periods, second function, Ni

Cost of capital: number, i

Find NPV: second function, NPV

NOW YOU NEED TO PLUG IN THE NUMBERS:

NPV for annuity:

Initial investment: 15000, minus sign, CFi

Annual cash inflow: 3000, CFi1

Number of periods: 8, second function, Ni

Cost of capital: 8, i

Find NPV: second function, NPV

= \$2,239.92

The above calculation makes it clear that project A is an acceptable project for ABC because the NPV is higher than zero (\$2,239.92).

### Comparing NPV and IRR

Theoretically, it is advisable to use Net Present Value method because NPV assumes that cash inflows are reinvested at cost of capital, which is more realistic than assumption made in Internal Rate of Return method (IRR) that cash inflows reinvested at IRR.

However, in real life, the IRR is more common because it considers the rate of return instead of dollar amount considered in the Net Present Value method and the former seems to be more intuitive to users of techniques. There are, however, ways to deal with shortcomings of IRR and therefore IRR is still can be considered a sophisticated and reliable technique.