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# NPV, APR, EAR Calculations

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1. What is the "value additivity corollary" with respect to evaluating ash flows over time?

2. What is the difference between APR (Annual Percentage rate) and EA (Effective Annual rate)?

#### Solution Preview

1)
Scenario 1
Suppose that that you have 2 small projects (and no others), each with its own cash flow. You could compute the NPV of each project separately, then add the NPVs together.

Scenario 2
Now, suppose you combine the combine the cash flows from the two small projects together into one huge project, and. You could compute the NPV of the huge project.

The value additivity corollary says that the total NPV Scenario 1 and Scenario 2 are the same. It does ...

#### Solution Summary

An explanation is given in 336 words. An Excel file showing all computations for an example of value additivity corollary, APR and EAR are provided.

\$2.19

## Interest rates and Time Value problem

1)
Calculate the future value of \$2000 in
a) 5 years at interest rate of 5% per year
b) 10 years at an interest rate of 5% per year
c) 5 years at an interest rate of 10% per year
d) why is the amount of interest earned in part (a) less than half the amount of interest earned in (b)

2)
You are thinking of retiring. Your retirement plan will either pay you \$250000 immediately on retirement or \$350000 five years after
date of retirement. Which alternative should you choose if interest rate is;
0% per year
8% per year
20% per year

3)
you have been offered a unique investment opportunity. If you invest \$10,000 today you will receive \$500 one year from now; \$1500 two years from now and \$10,000 ten years from now

what is the NPV of the opportunity if the interest rate is 6% per year? Should you take the opportunity?
what is the NPV of the opportunity if the interest rate is 2% per year? Should you take the opportunity?

4)
What is the present value of \$1000 paid at the end of each of the next 100 years if interest rate is 7% per year?

5)
you have found 3 investment choices for a one year deposit
****10% APR compounded monthly
****10% APR compounded annually
****9% APR compounded daily
Compute the EAR for each investment with 365 days in the year

6)Key Bank is offering a 30 year mortgage with an EAR of 5 and 3/8%. If I borrow \$ 150,000 what will be my monthly payment?

7)
if the rate of inflation is 5% what nominal interest rate is necessary for you to earn a 3% real interest rate on your investment

8) your best taxable investment has an EAR of 4%. Your best tax-free investment opportunity has an EAR of 3%.
If your tax rate is 30%, which opportunity provides the higher after-tax interest rate?

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