Question

*Solve without using Excel, write out the equations*

Suppose a project requires an initial cash outflow of $34,900. The project will last for four years with the annual cash flows given below. The required rate of return is 12%.

Year Cash Flow	Cash Flows
1	12,500
2	19,700
3	0
4	10,400

A) Compute the net present value of the project. Should the firm invest in this project based on net present value? Why?

B) Compute the internal rate of return. Should the firm invest in this project based on internal rate of return? Why?

C) Use a graph to show why the firm’s decisions in (1) and (2) are consistent or inconsistent. Be specific

D) Now suppose another project’s future annual cash flows are given below with an initial cash outflow $14,900.00). The required rate of return is 12%. Using a graph to explain why you cannot use IRR for capital budgeting in this case. (You do not need to compute anything here.)

Year	Cash Flow
1	12,500
2	12,500
3	12,500
4	12,500
5	12,500
6	12,500
7	-19,700
8	-20,000
9	-20,000
10	-20,000

Answer 1

(A) Calculation of NPV :

(amount in $)

Year (n)	Cashflow (a)	PVF@12%[1/(1+r)n] (b)	PV (a*b)
0	-34500	[1/(1+0.12)0] = 1.000	-34500
1	12500	[1/(1+0.12)1] = 0.893	11162.50
2	19700	[1/(1+0.12)2​​​​​​​] = 0.797	15700.90
3	0	[1/(1+0.12)3​​​​​​​] = 0.712	0
4	10400	[1/(1+0.12)4​​] = 0.636	6614.40
		NPV	-1022.20

Firm should not invest in this project because its NPV is negative i.e. -$1022.20.

(B) Computation of internal rate of return :

(amount in $)

Year (n)	Cashflow (a)	PVF@10%[1/(1+r)n] (b)	PV (a*b)	PVF@11%[1/(1+r)n] (c)	PV (a*c)
0	-34500	[1/(1+0.10)0​​​​​​​] = 1.000	-34500	[1/(1+0.11)0​​​​​​​] = 1.000	-34500
1	12500	[1/(1+0.10)1] = 0.909	11362.50	[1/(1+0.11)1] = 0.901	11262.50
2	19700	[1/(1+0.10)2​​​​​​​] = 0.826	16272.20	[1/(1+0.11)2​​​​​​​] = 0.812	15996.40
3	0	[1/(1+0.10)3​​​​​​​] = 0.751	0	[1/(1+0.11)3​​​​​​​] = 0.731	0
4	10400	[1/(1+0.10)4​​] = 0.683	7103.20	[1/(1+0.11)4​​] = 0.659	6853.60
		NPV at LR	237.65	NPV at HR	-387.50

IRR = Lower rate + [NPV at LR / (NPV at LR - (-NPV at HR))] * (Higher rate - Lower rate)

= 10 + [237.65 / (237.65 - (-387.50))] * (11-10)

= 10 +[0.380] * 1

= 10.38%

Firm should not opt this project because its IRR (10.38%) is less than required rate of return (12%).