Question

Project S costs $16,000 and is expected to produce cash flows of $5,000 per year for 6 years. What is the discounted payback period for this project if the cost of capital is 21%?

A) 3.92 years

B) 5.61 years

C) 4.86 years

D) 5.85 years

What is the NPV for this project is the cost capital is 21%?

A) $157.65

B) -$110.23

C) $199.36

D) $223.08

What is the NPV for this project if the cost of capital is 22%?

A) -$134.89

B) - $99.23

C) $111.67

D) -165.41

What is the IRR for this project?

A) 20.12%

B) 21.57

C) 21.88%

D) 22.13%

What is the MIRR for this project is the cost of capital is 21%?

A) 20.76%

B) 21.87%

C) 21.28%

D) 22.19%

Should we accept of reject this project if the cost of capital is 22 percent?

A) Reject since IRR < 0

B) Reject since NPV < 0

C) Accept since IRR > 0

D) Accept since NPV > 0

Answer 1

Answer to Question 1:

Present Value of Cash Inflow in Year 1 = $5,000/1.21
Present Value of Cash Inflow in Year 1 = $4,132.23

Present Value of Cash Inflow in Year 2 = $5,000/1.21^2
Present Value of Cash Inflow in Year 2 = $3,415.07

Present Value of Cash Inflow in Year 3 = $5,000/1.21^3
Present Value of Cash Inflow in Year 3 = $2,822.37

Present Value of Cash Inflow in Year 4 = $5,000/1.21^4
Present Value of Cash Inflow in Year 4 = $2,332.54

Present Value of Cash Inflow in Year 5 = $5,000/1.21^5
Present Value of Cash Inflow in Year 5 = $1,927.72

Present Value of Cash Inflow in Year 6 = $5,000/1.21^6
Present Value of Cash Inflow in Year 6 = $1,593.15

Company can recover initial investment of $14,629.93 ($4,132.3 + $3,415.07 + $2,822.37 + $2,332.54 + $1,927.72) in first 5 years and remaining $1,370.07 in 6th year

Discount Payback Period = 5 + $1,370.07 / $1,593.15
Discount Payback Period = 5.85 years

Answer to Question 2:

Net Present Value = -$16,000 + $5,000/1.21 + $5,000/1.21^2 + $5,000/1.21^3 + $5,000/1.21^4 + $5,000/1.21^5 + $5,000/1.21^6
Net Present Value = -$16,000 + $5,000 * (1 - (1/1.21)^6) / 0.21
Net Present Value = -$16,000 + $5,000 * 3.244615
Net Present Value = $223.08

Answer to Question 3:

Net Present Value = -$16,000 + $5,000/1.22 + $5,000/1.22^2 + $5,000/1.22^3 + $5,000/1.22^4 + $5,000/1.22^5 + $5,000/1.22^6
Net Present Value = -$16,000 + $5,000 * (1 - (1/1.22)^6) / 0.22
Net Present Value = -$16,000 + $5,000 * 3.166918
Net Present Value = -$165.41

Answer to Question 4:

Let IRR be i%

Net Present Value = -$16,000 + $5,000/(1+i) + $5,000/(1+i)^2 + $5,000/(1+i)^3 + $5,000/(1+i)^4 + $5,000/(1+i)^5 + $5,000/(1+i)^6
0 = -$16,000 + $5,000/(1+i) + $5,000/(1+i)^2 + $5,000/(1+i)^3 + $5,000/(1+i)^4 + $5,000/(1+i)^5 + $5,000/(1+i)^6

Using financial calculator, i = 21.57%

IRR of the project = 21.57%

Answer to Question 5:

Future Value of Cash Inflows = $5,000*1.21^5 + $5,000*1.21^4 + $5,000*1.21^3 + $5,000*1.21^2 + $5,000*1.21 + $5,000
Future Value of Cash Inflows = $5,000 * (1.21^6 - 1) / 0.21
Future Value of Cash Inflows = $5,000 * 10.182992
Future Value of Cash Inflows = $50,914.96

MIRR = (Future Value of Cash Inflows / Present Value of Cash Outflow)^(1/Period) - 1
MIRR = ($50,914.96 / $16,000)^(1/6) - 1
MIRR = 3.182185^(1/6) - 1
MIRR = 1.2128 - 1
MIRR = 0.2128 or 21.28%

Answer to Question 6:

NPV at cost of capital of 22% is negative; therefore, Reject since NPV < 0