Question

You are evaluating an investment project, Project YY, with the following Cash

flows

period cash flow

0 -$ 100,000

1 43,798

2 43,798

3 43,798

Required: Calculate the following:

a. Payback period

b. Discounted payback period, assuming a 10% cost of capital

c. Discounted payback period, assuming a 14% cost of capital

d. Net present value, assuming a 14% cost of capital

Answer 1

1.) Payback Period.

This the amount of time it will take for the investment to recover the initial cost.

Year 1-43,798

Year 2-87,596;

Remaining amount to reach 100,000;

100,000-87596=12,404; express it as a fraction of year 3 cash flow to find years.

$\frac{12,404}{43,798}=0.28$

Total payback=2+0.28=2.28 years.

2.) Discounted payback@10%

$Year 0=-100,000\times\frac{1}{(1.1)^{0}}=-100,000$

$Year 1=43,798\times\frac{1}{(1.1)^{1}}=39,816$

$Year 2=43,798\times\frac{1}{(1.1)^{2}}=36,197$

$Year 3=43,798\times\frac{1}{(1.1)^{3}}=32,906$

By year 2, the balance will be:

-100,000+39,816+36,197=23,987

Express as fraction to find year.

$\frac{23,987}{32,906}=0.73$

Discounted payback Period=2+0.73=2.73 years

3. Discounted Payback period@14%

$Year 0=-100,000\times\frac{1}{(1.1)^{0}}=-100,000$

$Year 1=43,798\times\frac{1}{(1.14)^{1}}=38,419$

$Year 2=43,798\times\frac{1}{(1.14)^{2}}=33,701$

$Year 3=43,798\times\frac{1}{(1.14)^{3}}=29,562$

By year 2, the balance will be:

-100,000+38,419+33,701=27,880

Express as fraction to find year.

$\frac{27,880}{32,906}=0.64$

Discounted payback Period=2+0.64=2.64 years

4.) NPV@14%

Sum all present values for 3 above.

-100,000+38,419+33,701+29,562=1,682

NPV=1,682