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4 years ago

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Assignment: Capital Budgeting Decisions Your company is considering undertaking a project to expand an existing product line. Th

e required rate of return on the project is 8% and the maximum allowable payback period is 3 years.
time 0 1 2 3 4 5 6
Cash flow $ 10,000 2,400 4,800 3,200 3,200 2,800 2,400
Evaluate the project using each of the following methods. For each method, should the project be accepted or rejected? Justify your answer based on the method used to evaluate the project’s cash flows.
A. Payback period
B. Internal Rate of Return (IRR)
C. Simple Rate of Return
D. Net Present Value

1 answer:

expeople1 [14]4 years ago

3 0

Answer:

A. Payback period

payback period = 2.875 years, therefore, the project should be accepted because the payback period is less than 3 years.

B. Internal Rate of Return (IRR)

IRR = 22.69%, therefore, the project should be accepted since the IRR is higher than the required rate of return (8%).

C. Simple Rate of Return

simple rate of return = 18%, therefore, the project should be accepted because the simple rate of return is higher than the required rate of return.

D. Net Present Value

NPV = $4,647.85 , therefore, the project should be accepted since the NPV is positive.

Explanation:

year cash flow

0 -$10,000

1 $2,400

2 $4,800

3 $3,200

4 $3,200

5 $2,800

6 $2,400

discount rate 8%

I used a financial calculator to determine the NPV and IRR.

Payback period = $10,000 - $2,400 - $4,800 = $2,800 / $3,200 = 0.875

payback period = 2.875 years

simple rate of return:

average cash flow = ($2,400 + $4,800 + $3,200 + $3,200 + $2,800 + $2,400) / 6 = $3,467

depreciation expense per year = $10,000 / 6 = $1,667

simple rate of return = ($3,467 - $1,667) / $10,000 = 18%

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Explanation:

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$V(n)=(1+R)^nP$

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$R$ is the annual interest rate,

$P$ is the principal investment.

We know the following:

$25000=(1+0.06)^n \times 10000$

And we want to clear the value <em>n</em> from the equation.

The problem can be resolved as follows.

<u>First step:</u> divide each member of the equation by $10,000$ :

$\frac{ 25000}{10000}=(1+0.06)^n \times \frac{ 10000}{10000}$

$2.5=(1.06)^n$

<u>Second step:</u> apply logarithms to both members of the equation:

$log(2.5)=log (1.06)^n$

<u>Third step:</u> apply the logarithmic property $logA^n=n.logA$ in the second member of the equation:

$log(2.5)=n.log (1.06)$

Fourth step: divide both members of the equation by $log1.06$

$\frac{log(2.50)}{log (1.06)} =n$

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The answer is 72.9 dollars.

Explanation:

The reserve ratio of 10% means that bank must keep 10% percent of amount deposited in bank to meet emergency payments and can lend the remaining 90% to other banks. So the second bank can lend 81 dollars that is 90% of 81 dollars. As per this rule second bank has 72.9 dollars (90% of 81) to lend.

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Answer:

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b(i) Standard deviation of the portfolio = 30.00%

b(ii) Standard deviation of the portfolio = 4.00%

b(iii) Standard deviation of the portfolio = 21.40%

Explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

Here are returns and standard deviations for four investments.

Return (%) Standard Deviation (%)

Treasury bills 4.5 0

Stock P 8.0 14

Stock Q 17.0 34

Stock R 21.5 26

Calculate the standard deviations of the following portfolios.

a. 50% in Treasury bills, 50% in stock P. (Enter your answer as a percent rounded to 2 decimal places.)

b. 50% each in Q and R, assuming the shares have:

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ii. perfect negative correlation

iii. no correlation

(Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

The explanation to the answer is now provided as follows:

a. Calculate the standard deviations of 50% in Treasury bills, 50% in stock P. (Enter your answer as a percent rounded to 2 decimal places.)

Since there is no correlation between Treasury bills and stocks, it therefore implies that the correlation coefficient between the Treasury bills and stock P is zero.

The standard deviation between the Treasury bills and stock P can be calculated by first estimating the variance of their returns using the following formula:

Portfolio return variance = (WT^2 * SDT^2) + (WP^2 * SDP^2) + (2 * WT * SDT * WP * SDP * CFtp) ......................... (1)

Where;

WT = Weight of Stock Treasury bills = 50%

WP = Weight of Stock P = 50%

SDT = Standard deviation of Treasury bills = 0

SDP = Standard deviation of stock P = 14%

CFtp = The correlation coefficient between Treasury bills and stock P = 0.45

Substituting all the values into equation (1), we have:

Portfolio return variance = (50%^2 * 0^2) + (50%^2 * 14%^2) + (2 * 50% * 0 * 50% * 14% * 0) = 0.49%

Standard deviation of the portfolio = (Portfolio return variance)^(1/2) = (0.49%)^(1/2) = (0.49)^0.5 = 7.00%

b. 50% each in Q and R

To calculated the standard deviation 50% each in Q and R, we first estimate the variance using the following formula:

Portfolio return variance = (WQ^2 * SDQ^2) + (WR^2 * SDR^2) + (2 * WQ * SDQ * WR * SDR * CFqr) ......................... (2)

Where;

WQ = Weight of Stock Q = 50%

WR = Weight of Stock R = 50%

SDQ = Standard deviation of stock Q = 34%

SDR = Standard deviation of stock R = 26%

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This implies that:

CFqr = The correlation coefficient between stocks Q and = 1

Substituting all the values into equation (2), we have:

Portfolio return variance = (50%^2 * 34%^2) + (50%^2 * 26%^2) + (2 * 50% * 34% * 50% * 26% * 1) = 9.00%

Standard deviation of the portfolio = (Portfolio return variance)^(1/2) = (9.00%)^(1/2) = (9.00%)^0.5 = 30.00%

b(ii). assuming the shares have perfect negative correlation

This implies that:

CFqr = The correlation coefficient between stocks Q and = -1

Substituting all the values into equation (2), we have:

Portfolio return variance = (50%^2 * 34%^2) + (50%^2 * 26%^2) + (2 * 50% * 34% * 50% * 26% * (-1)) = 0.16%

Standard deviation of the portfolio = (Portfolio return variance)^(1/2) = (0.16%)^(1/2) = (0.16%)^0.5 = 4.00%

b(iii). assuming the shares have no correlation

This implies that:

CFqr = The correlation coefficient between stocks Q and = 0

Substituting all the values into equation (2), we have:

Portfolio return variance = (50%^2 * 34%^2) + (50%^2 * 26%^2) + (2 * 50% * 34% * 50% * 26% * 0) = 4.58%

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