Chapter 5, Problem 10QP

a.

Summary Introduction

To determine: Internal rate of return.

Internal Rate of Return (IRR):

IRR is the rate at which the future cash inflows will be equal to the initial cash outflows. It is the discounting rate.

Answer to Problem 10QP

Solution:

Compute the IRR.

Explanation of Solution

• The excel spreadsheet is used to calculate the internal rate of return.
• The IRR function is used to compute the internal rate of return.

Conclusion

Hence, internal rate of return is 12%.

b.

Summary Introduction

To explain: Whether Person X should accept this offer or not on 10% discount rate.

Answer to Problem 10QP

Solution:

Person X should accept this offer on 10% discount rate.

Explanation of Solution

One should accept this offer because internal rate of return is 12% which is higher than the discount rate of 10%. It means that the current project will fetch profit for the company.

Conclusion

Hence, Person X should accept this project.

c.

Summary Introduction

To explain: Whether one should accept this offer or not on 20% discount rate.

Answer to Problem 10QP

Solution:

Person X should not accept this offer on 20% discount rate.

Explanation of Solution

Person X should not accept this offer because internal rate of return is 12% which is lower than the discount rate of 20%. It means that the current project will not be able to earn even what is initially invested in the project.

Conclusion

Hence, Person X should not accept this project.

d.

Summary Introduction

To determine: NPV at 10% and 20% discount rate.

Net Present Value (NPV):

Net present value refers to the present value of all the future cash flow that is adjusted according to the time value of money.

Explanation of Solution

Compute the NPV.

For discount rate of 10%:

Given,

C₀ is $9,400.

CF₁ is $4,500.

CF₂ is $3,100.

CF₃ is $2,400.

CF₄ is $1,800.

r is 10%.

Solution:

Formula to compute NPV,

$NPV=\frac{C{F}_1}{{\left(1+r\right)}^1}+\frac{C{F}_2}{{\left(1+r\right)}^2}+\frac{C{F}_3}{{\left(1+r\right)}^3}+\frac{C{F}_4}{{\left(1+r\right)}^4}-C_0$

Where,

• C₀ is initial investment.
• CF₁ is cash inflow in first year.
• CF₂ is cash inflow in second year.
• CF₃ is cash inflow in third year.
• CF₄ is cash inflow in fourth year.
• r is discount rate.

Substitute, $9,400 for C₀, $4,500 for CF₁, $3,100 for CF_2, $2,400 for CF₃,$1,800 for CF₄ and 10% for r.

$\begin{array}{c}NPV=\frac{\$4,500}{{\left(1+0.1\right)}^1}+\frac{\$3,100}{{\left(1+0.1\right)}^2}+\frac{\$2,400}{{\left(1+0.1\right)}^3}+\frac{\$1,800}{{\left(1+0.1\right)}^4}-\$9,400\\ =\$4,090.91+\$2,561.98+\$1,803.16+\$1,229.42-\$9,400\\ =\$9,685.47-\$9,400\\ =\$285.47\end{array}$

The NPV for discount rate of 10% is $285.47.

For discount rate of 20%:

Given,

C₀ is $9,400.

CF₁ is $4,500.

CF₂ is $3,100.

CF₃ is $2,400.

CF₄ is $1,800.

r is 20%.

Formula to compute NPV,

$NPV=\frac{C{F}_1}{{\left(1+r\right)}^1}+\frac{C{F}_2}{{\left(1+r\right)}^2}+\frac{C{F}_3}{{\left(1+r\right)}^3}+\frac{C{F}_4}{{\left(1+r\right)}^4}-C_0$

Where,

• C₀ is initial investment.
• CF₁ is cash inflow in first year.
• CF₂ is cash inflow in second year.
• CF₃ is cash inflow in third year.
• CF₄ is cash inflow in fourth year.
• r is discount rate.

Substitute, $9,400 for C₀, $4,500 for CF₁, $3,100 for CF_2, $2,400 for CF₃,$1,800 for CF₄ and 20% for r.

$\begin{array}{c}NPV=\frac{\$4,500}{{\left(1+0.2\right)}^1}+\frac{\$3,100}{{\left(1+0.2\right)}^2}+\frac{\$2,400}{{\left(1+0.2\right)}^3}+\frac{\$1,800}{{\left(1+0.2\right)}^4}-\$9,400\\ =\$3,750+\$2,152.78+\$1,388.89+\$868.06-\$9,400\\ =\$8,159.73-\$9,400\\ =-\$1,240.27\end{array}$

The NPV for discount rate of 20% is −$1,240.27.

Conclusion

Hence, NPV for discount rate of 10% and 20% is $285.47 and -$1,240.27 respectively.

e.

Summary Introduction

To explain: Whether NPV rule is consistent with IRR rule or not.

Answer to Problem 10QP

Solution:

Yes, NPV rule is consistent with the internal rate of return method.

Explanation of Solution

NPV rule is consistent with IRR because according to both the methods, project with 10% discount rate is accepted and project with 20% discount rate should be discarded. It is because project is giving positive return only when 10% discount rate is used otherwise it is giving negative returns and it is consistent because, only once the signs of the cash flows changes.

Conclusion

Hence, NPV is consistent with the IRR rule.