Question

First five years of a business:

Cost of Capital 8.00%

Initial Investment $(40,000)

Year 1 Cash Flows 8,000

Year 2 Cash Flows 9,200

Year 3 Cash Flows 10,000

Year 4 Cash Flows 12,000

Year 5 Cash Flows 14,500

1. Calculate the net present value (NPV), internal rate of return (IRR) and payback period.

2. Assume you can sell the business in year 5 for 10x’s annual cash flow. Calculate the net present value (NPV) and internal rate of return (IRR).

3. Suppose the cost of capital is 12% instead of 8%.....

4. What are the net present value (NPV) and internal rate of return (IRR) for the initial cash flow numbers with the new cost of capital?

5. Now, assume you can sell the business in year 5 for 10x’s annual earnings. What are the net present value (NPV) and internal rate of return (IRR) with the new cost of capital?

Answer 1

Year	Cash Flow ($)	Cumulative Cashflow
0	-40000	-40000
1	8000	-32000
2	9200	-22800
3	10000	-12800
4	12000	-800
5	14500	13700

Cost of Capital = 8%

NPV

NPV = -40000 + 8000(P/F,8%,1)+ 9200(P/F,8%,2)+ 10000(P/F,8%,3)+ 12000(P/F,8%,4)+ 14500(P/F,8%,5)

NPV = -40000 + 8000*0.9259+ 9200*0.8573+ 10000*0.7938+ 12000*0.7350+ 14500*0.6806

NPV = -40000 + 7407.2 + 7887.16 + 7938+ 8820+ 9528.4

NPV = $1580.76

IRR

NPV = -40000 + 8000(P/F,IRR,1)+ 9200(P/F,IRR,2)+ 10000(P/F,IRR,3)+ 12000(P/F,IRR,4)+ 14500(P/F,IRR,5)

For IRR, NPV =0

0 = -40000 + 8000(P/F,IRR,1)+ 9200(P/F,IRR,2)+ 10000(P/F,IRR,3)+ 12000(P/F,IRR,4)+ 14500(P/F,IRR,5)

Using Hit and Trial method or Excel IRR function

IRR = 9.35%

Payback Period

Here the Investment of 40000 is paid somewhat between 4 and 5 years

Payback period = 4 + 800/14500 = 4.055 years

If Business can be sold in year 5 for 10 time annual cash flow means for $ 145000

Year	Cash Flow ($)	Cumulative Cashflow
0	-40000	-40000
1	8000	-32000
2	9200	-22800
3	10000	-12800
4	12000	-800
5	14500	13700
5	145000	158700

NPV

NPV = -40000 + 8000(P/F,8%,1)+ 9200(P/F,8%,2)+ 10000(P/F,8%,3)+ 12000(P/F,8%,4)+ 14500(P/F,8%,5) + 145000(P/F,8%,5)

NPV = -40000 + 8000*0.9259+ 9200*0.8573+ 10000*0.7938+ 12000*0.7350+ 14500*0.6806 + 145000*0.6806

NPV = -40000 + 7407.2 + 7887.16 + 7938+ 8820+ 9528.4 + 98687

NPV = $100267.76

IRR

NPV = -40000 + 8000(P/F,IRR,1)+ 9200(P/F,IRR,2)+ 10000(P/F,IRR,3)+ 12000(P/F,IRR,4)+ 159000(P/F,IRR,5)

For IRR, NPV =0

0 = -40000 + 8000(P/F,IRR,1)+ 9200(P/F,IRR,2)+ 10000(P/F,IRR,3)+ 12000(P/F,IRR,4)+ 159000(P/F,IRR,5)

Using Hit and Trial method or Excel IRR function

IRR = 45.64%

Cost of Capital = 12%

NPV

NPV = -40000 + 8000(P/F,12%,1)+ 9200(P/F,12%,2)+ 10000(P/F,12%,3)+ 12000(P/F,12%,4)+ 14500(P/F,12%,5)

NPV = -40000 + 8000*0.8929+ 9200*0.7972+ 10000*0.7118+ 12000*0.6355+ 14500*0.5674

NPV = -40000 + 7143.2 + 7334.24 + 7118+ 7626+ 8227.3

NPV = -$2551.26

IRR

NPV = -40000 + 8000(P/F,IRR,1)+ 9200(P/F,IRR,2)+ 10000(P/F,IRR,3)+ 12000(P/F,IRR,4)+ 14500(P/F,IRR,5)

For IRR, NPV =0

0 = -40000 + 8000(P/F,IRR,1)+ 9200(P/F,IRR,2)+ 10000(P/F,IRR,3)+ 12000(P/F,IRR,4)+ 14500(P/F,IRR,5)

Using Hit and Trial method or Excel IRR function

IRR = 9.35%

If Business can be sold in year 5 for 10 time annual cash flow means for $ 145000

Year	Cash Flow ($)	Cumulative Cashflow
0	-40000	-40000
1	8000	-32000
2	9200	-22800
3	10000	-12800
4	12000	-800
5	14500	13700
5	145000	158700

NPV

NPV = -40000 + 8000(P/F,12%,1)+ 9200(P/F,12%,2)+ 10000(P/F,12%,3)+ 12000(P/F,12%,4)+ 159000(P/F,12%,5)

NPV = -40000 + 8000*0.8929+ 9200*0.7972+ 10000*0.7118+ 12000*0.6355+ 159000*0.5674

NPV = -40000 + 7143.2 + 7334.24 + 7118+ 7626+ 90216.6

NPV = $79438.04

IRR

NPV = -40000 + 8000(P/F,IRR,1)+ 9200(P/F,IRR,2)+ 10000(P/F,IRR,3)+ 12000(P/F,IRR,4)+ 159000(P/F,IRR,5)

For IRR, NPV =0

0 = -40000 + 8000(P/F,IRR,1)+ 9200(P/F,IRR,2)+ 10000(P/F,IRR,3)+ 12000(P/F,IRR,4)+ 159000(P/F,IRR,5)

Using Hit and Trial method or Excel IRR function

IRR = 45.64%