Question #305809

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


1
Expert's answer
2022-03-04T08:29:39-0500

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.

12,40443,798=0.28\frac{12,404}{43,798}=0.28

Total payback=2+0.28=2.28 years.


2.) Discounted payback@10%


Year0=100,000×1(1.1)0=100,000Year 0=-100,000\times\frac{1}{(1.1)^{0}}=-100,000

Year1=43,798×1(1.1)1=39,816Year 1=43,798\times\frac{1}{(1.1)^{1}}=39,816

Year2=43,798×1(1.1)2=36,197Year 2=43,798\times\frac{1}{(1.1)^{2}}=36,197

Year3=43,798×1(1.1)3=32,906Year 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.

23,98732,906=0.73\frac{23,987}{32,906}=0.73


Discounted payback Period=2+0.73=2.73 years


3. Discounted Payback period@14%



Year0=100,000×1(1.1)0=100,000Year 0=-100,000\times\frac{1}{(1.1)^{0}}=-100,000

Year1=43,798×1(1.14)1=38,419Year 1=43,798\times\frac{1}{(1.14)^{1}}=38,419

Year2=43,798×1(1.14)2=33,701Year 2=43,798\times\frac{1}{(1.14)^{2}}=33,701

Year3=43,798×1(1.14)3=29,562Year 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.

27,88032,906=0.64\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



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