Question

5 (13pt) What is the payback period of the following investment when a) i= 0% and b) i=10%/year?

Site	Initial cost ($)	Annual cost ($)	Annual Income ($)	Salvage value	Max life time
A	100000	10000	30000	50000	10 yrs

Answer 1

Payback is the amount of time it takes to recover the cost of an investment. It is the length of time it takes an investment to reach its breakeven point. The desirability of an investment is directly related to its payback period, Shorter paybacks mean more attractive investments.

Since it is not given we will assume that salvage value inflow occurs at the end of 10 years.

a) At 0% interest rate we are not considering the time value of money. The annual cost is $10,000 and annual income is $30,000 so it leaves net inflow of $20,000. It has an even net cash inflow of $20,000 so we can use the following formula:

Payback period = Initial investment/Annual cash flow

= 100,000/20,000

= 5 years.

b) At a 10% interest rate, we will have to calculate it's present value and then payback period.

Present value is the value in the present, of a sum of money, in contrast to some future value it will have when it has been invested at compound interest.

Present value = Future value/(1 + interest rate)^year

So for 1st-year net cash flow is $20,000

Preset value = 20,000/(1+ 10%)^1

= $18,181.82

For 2nd year:

Present value = 20,000/(1+ 10%)^2

= $16,528.93

For 3rd year:

Present value = 20,000/(1+ 10%)^3

= $15,026.30

For 4th year:

Present value = 20,000/(1+ 10%)^4

= $13,660.27

And so on. In table form

Year	Cash flow	PV of revenues	Cumulitive cash flow
0	-$100,000.00	-100,000.00	-100,000.00
1	$20,000	$18,181.82	-$81,818.18
2	$20,000	$16,528.93	-$65,289.26
3	$20,000	$15,026.30	-$50,262.96
4	$20,000	$13,660.27	-$36,602.69
5	$20,000	$12,418.43	-$24,184.26
6	$20,000	$11,289.48	-$12,894.79
7	$20,000	$10,263.16	-$2,631.62
8	$20,000	$9,330.15	$6,698.52
9	$20,000	$8,481.95	$15,180.48
10	$50,000	$19,277.16	$34,457.64

Now to find out the payback period:

Step 1: We must pick the year in which the outflows have become positive. In other words, the year with the last negative outflow has to be selected. So, in this case, it will be year seven.

Step 2: Divide the total cumulative flow in the year in which the cash flows became positive (Seven) by the total flow of the consecutive year.

In this way we divide what's remaining to recover with what's coming the given year, Its line the method we used to calculate a

= 7 + (2,631.62/9,330.15)

= 7.28 years