Question

A project has an initial cost of $40,000, expected net cash inflows of $9,000 pr year for 7 years, and cost of capital of 11%.

a) What is the project's NPV? (Hint: Begin by constructing a time line.)

b) What is the project's IRR?

c) What is the project's MIRR?

d) What is the project's PI?

e) What is the project's payback period?

f) What is the project's discounted payback period?

Show your steps of solving the problems.

Answer 1

a)

NPV = Cash outflow + Cash Inflow 1 / (1 + Cost of capital)¹+....+ Cash Inflow 7 / (1 + Cost of capital)⁷

NPV = -$40,000 + $9000 / (1 + 11%)¹ + ... + $9000 / (1 + 11%)⁷

Using PVIFA formula = (1 - (1 + interest rate)^{-no of periods} / interest rate)

NPV = -$40,000 + (1 - (1 + 11%)^-7 / 11%) * $9000

NPV = -$40,000 + $42,409.77

NPV = $2409.77

b)

NPV = Cash outflow + Cash Inflow 1 / (1 + IRR )¹+....+ Cash Inflow 7 / (1 + IRR)⁷

For IRR we need to set NPV = 0

0 = -$40,000 + $9000 / (1 + IRR )¹+ $9000(1 + IRR)² + $9000(1 + IRR)³ + $9000(1 + IRR)⁴ + $9000(1 + IRR)⁵ + $9000(1 + IRR)⁶ + $9000(1 + IRR)⁷

Using the Texas instruments BA 2 plus calculator

CFo =-40,000 PRESS ENTER

C01 = 9000 PRESS ENTER

F01 = 7 PRESS ENTER

CPT ---> IRR

We get IRR = 12.84%

c)

To calculate the terminal cashflow we assume the reinvestment rate = 11%

Terminal value of cash flow = $9000 * (1 + 11%)¹+ $9000 * (1 + 11%)² + $9000 * (1 + 11%)³ + $9000 * (1 + 11%)⁴ + $9000 * (1 + 11%)⁵ + $9000 * (1 + 11%)⁶ + $9000 * (1 + 11%)⁷

Using FVIFA formula = (((1 + interest rate)^{no of periods} - 1) / interest rate)

Terminal value of cash flow = $9000 * (((1 + 11%)⁷ - 1) / 11%)

Terminal value of cash flow = $88,049.47

Present value of Cash Outflow = $40,000

MIRR = (Terminal value of cash flow / Present value of Cash Outflow)^{1 / no of periods} -1

MIRR = ($88,049.47 / $40,000)^1/7 -1

MIRR = 1.1193 -1

MIRR = 0.1193 or 11.93%

d)

Present value of Cash inflows = Cash Inflow 1 / (1 + IRR )¹+....+ Cash Inflow 7 / (1 + IRR)⁷

Present value of Cash inflows = $9000 / (1 + IRR )¹+ $9000(1 + IRR)² + $9000(1 + IRR)³ + $9000(1 + IRR)⁴ + $9000(1 + IRR)⁵ + $9000(1 + IRR)⁶ + $9000(1 + IRR)⁷

Using PVIFA formula = (1 - (1 + interest rate)^{-no of periods} / interest rate)

Present value of Cash inflows = (1 - (1 + 11%)^-7 / 11%) * $9000

Present value of Cash inflows = $42,409.77

Initial Outlay = $40,000

Profitability index = Present value of Cash inflows / Initial Outlay

Profitability index = $42,409.77 / $40,000

Profitability index = 1.06

e)

Cumulative Net Cashflow for year 1 = Cumulative Net Cashflow for year 0 + Net Cashflow for year 1

Cumulative Net Cashflow for year 1 = -$40,000 + $9000

Cumulative Net Cashflow for year 1 = -$31,000

Year	0	1	2	3	4	5	6	7
Net Cashflow	-$40,000	$9,000	$9,000	$9,000	$9,000	$9,000	$9,000	$9,000
Cumulative Net Cashflow	-$40,000	-$31,000	-$22,000	-$13,000	-$4,000	$5,000	$14,000	$23,000

The cumulative cashflow turns positive in year 5

Payback period = full years until recovery + (unrecovered cost at beginning of recovery year / cash flow during recovery year)

Payback period = 4 + ($4000 / $9000)

Payback period = 4.44 years

f)

Cumulative Net Cashflow for year 1 = Cumulative Net Cashflow for year 0 + Discounted Net Cashflow for year 1

Cumulative Net Cashflow for year 1 = -$40,000 + $8,108.11

Cumulative Net Cashflow for year 1 = -$31,891.89

Year	0	1	2	3	4	5	6	7
Net Cashflow	-$40,000	$9,000	$9,000	$9,000	$9,000	$9,000	$9,000	$9,000
Discounted Net Cashflow	-$40,000.00	$8,108.11	$7,304.60	$6,580.72	$5,928.58	$5,341.06	$4,811.77	$4,334.93
Cumulative Net Cashflow	-$40,000.00	-$31,891.89	-$24,587.29	-$18,006.57	-$12,077.99	-$6,736.93	-$1,925.16	$2,409.77

The cumulative cashflow turns positive in year 7

Payback period = full years until recovery + (unrecovered cost at beginning of recovery year / cash flow during recovery year)

Payback period = 6 + ($1,925.16 / $4,334.93)

Payback period = 6.44 years