Question

The Renn project costs $26,000, and its expected net cash inflows are $7,800 per year for 8 years. What is the project's payback period? What is the project's net present value (NPV), profitability index (PI), and internal rate of return (IRR) assuming a cost of capital of 10%? Calculate the project's modified internal rate of return (MIRR) assuming a cost of capital of 10%. What is the payback period of the Renn project?

Answer 1

Cost of Project = $26,000
Expected Net Cash Inflows = $7,800
Life of Project = 8 years

Answer a.

Payback Period = Cost of Project / Expected Net Cash Inflows
Payback Period = $26,000 / $7,800
Payback Period = 3.33 years

Answer b.

Cost of Capital = 10%

Present Value of Cash Inflows = $7,800 * PVIFA(10%, 8)
Present Value of Cash Inflows = $7,800 * (1 - (1/1.10)^8) / 0.10
Present Value of Cash Inflows = $7,800 * 5.33493
Present Value of Cash Inflows = $41,612.45

Net Present Value = Present Value of Cash Inflows - Cost of Project
Net Present Value = $41,612.45 - $26,000
Net Present Value = $15,612.45

Answer c.

Profitability Index = Present Value of Cash Inflows / Cost of Project
Profitability Index = $41,612.45 / $26,000
Profitability Index = 1.60

Answer d.

Let IRR be i%

NPV = -$26,000 + $7,800 * PVIFA(i%, 8)
0 = -$26,000 + $7,800 * PVIFA(i%, 8)

Using financial calculator:
N = 8
PV = -26000
PMT = 7800
FV = 0

I = 24.95%

IRR of the project is 24.95%

Answer e.

Future Value of Cash Inflows = $7,800*1.10^7 + $7,800*1.10^6 + ... + $7,800*1.10 + $7,800
Future Value of Cash Inflows = $7,800 * (1.10^8 - 1) / 0.10
Future Value of Cash Inflows = $7,800 * 11.43589
Future Value of Cash Inflows = $89,199.942

MIRR = (Future Value of Cash Inflows / Present Value of Cash Outflow)^(1/8) - 1
MIRR = ($89,199.942 / $26,000)^(1/8) - 1
MIRR = 3.430767^(1/8) - 1
MIRR = 1.1666 - 1
MIRR = 0.1666 or 16.66%