Question

(1).     What is the payback period of an investment with the following cash flows?

            Year      Cash Flow

            0            -60,000

            1            30,000

            2            20,000

            3            15,000

            4            10,000

            5            5,000

(2). A project has the following cash flows:

Year                     Cash Flow

0                          -$4,000

1                            2,000

2                            2,000

3                            2,000

4                            2,000

Its cost of capital is 10 percent. What is the project’s discounted payback period?

Answer 1

(1) Payback period calculates the time required to generate future cash flow which equals initial cost.

Cost = 60000

Year	Cashflow	Cumulative Cash flow	Time Completed
1	30000	30000	1
2	20000	30000 +20000 =50000	1
3	15000	50000 + 10000 = 60000	10000/15000 =0.67
4	10000
5	5000

We can see only 10000 is consumed out of 15000 to make it equal to the cost of 60000.

The time required to achieve cashflow of 10000 = 10000/15000 = 0.67

Payback Period = 1 +1 +0.67 =2.67 years Answer

(2)

Discounted Payback period calculates the time required to generate the present value of future cash flow which equals initial cost.

Cost = 4000

Cost of capital = 10%

Year	Cashflow	PV of Cashflow	Cumulative PV Cashflow	Time completed
1	2000	2000/(1+0.1)^1= 1818.18	1818.18	1
2	2000	2000/(1+0.1)^2= 1652.90	1818.18+1652.90 = 3471.08	1
3	2000	2000/(1+0.1)^3= 1502.63	3471.08 + 528.92 =4000	528.92/1502.63= 0.35
4	2000	2000/(1+0.1)^4= 1366.03

We can see only 528.92 is consumed out of 1502.63 to make it equal to the cost of 4000.

The time required to achieve cashflow of 528.92 = 528.92/1502.63 = 0.35

Payback Period = 1 +1 +0.35 =2.35 years Answer

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