Question

Your company is considering a project which has the expected cash flows as follows.

year	0	1	2	3	4	5	6	7	8	9	10
cash flow	-500	90	100	150	180	190	140	100	80	60	-50

The required return for the project is 15% per annum.

(1) What is the NPV?
(2) What are 2 IRRs?
(3) Draw the NPV profile

(4) What are the MIRR?
(5) Should your company take this project?

Answer 1

1.  PV of cash flows = CFt/ (1+k)^t or CFt x Discount Factor

where CFt is cash flow in year t, k = Cost of capital (WACC) & t is the year of Cash flow

NPV = Sum of PV of all future cash flows - Sum of PV of all Investment

The NPV of the project = 78.93

Year	Cash Flow	Discount Factor @ 15%	Discounted CF
0	-500	1.000	-500.00
1	90	0.870	78.30
2	100	0.756	75.60
3	150	0.658	98.70
4	180	0.572	102.96
5	190	0.497	94.43
6	140	0.432	60.48
7	100	0.376	37.60
8	80	0.327	26.16
9	60	0.284	17.04
10	-50	0.247	-12.35
NPV			78.92

2. The project has 2 IRRs (Since their is an investment in the last year of the project)

Can be found using the excel function for IRR

IRR = 19.45%

IIR 2 = - 59.90%

3. NPV Profile chart - NPV at various levels of discount rate (ranging from 0% to 30%

4. MIRR = (FVCF / PVCF)^(1/n) - 1

Where:

FVCF – the future value of positive cash flows discounted at the reinvestment rate

PVCF – the present value of negative cash flows discounted at the financing rate

n – the number of periods

FVCF = CFt x (1+ Investment Rate)^ (Time left for project)

Year	Cash Flow	Future Value of Positive Cash Flows at 15%	Present Value of Negative Cash Flows @15%
0	-500		-500.00
1	90	316.609
2	100	305.902
3	150	399.003
4	180	416.351
5	190	382.158
6	140	244.861
7	100	152.088
8	80	105.800
9	60	69.000
10	-50		-12.36
	PV	2391.77	-512.36

MIRR = (FVCF / PVCF)^(1/n) - 1

MIRR = (2391.77/ 512.36)^ (1/10) -1

= (4.668^(1/10)) -1

= 1.16658 -1

MIRR = 16.66%

5. The company should go ahead with the project as NPV is greater than 0 and MIRR is greater than discount rate