Problem Set # 2 - Time Value of Money

• What is anopportunity cost rate?How is this rate used in discounted cash flow analysis? Is the opportunity rate a single number that is used to evaluate all potential investments?

• If a firm's earnings per share grew from $1 to $2over a 10-year period, thetotal growthwould be100%, but theannual growth ratewould beless than 10%. True or false? Explain.

(Hint: Solve for the interest rate. Make sure you put the PV or FV as a negative number.)

• Would you rather have a savings account that pays5% interest compounded semiannually or one that paysinterest compounded daily? Explain.

• We sometimes need to find out how long it will take a sum of money (or something else, such as earnings, population, or prices) to grow to some specified amount. For example, if a company's sales are growing at a rate of 20% how long will it take sales to double?

(Hint: Assume that your current level of sales is at 100 units and find out how long it will take to get to 200 units if sales grow at 20% each year. Solve for N. Make sure you put the PV or FV as a negative number.)

• If you want an investment to double in3 years, what interest rate must it earn? (Hint: Solve for the interest rate)

• Find theFV of$1000invested to earn10% annually5 yearsfrom now. (Assume this is a single payment not an annuity).

• Find thePV of$1000due in5 yearsif the discount rate is10% per year. (Assume this is a single payment not an annuity).

• What is the future value of a7%, 5-yearordinary annuity that pays$300 each year?

• While Jack was a student at the University of Georgia she borrowed$12,000in student loans at an annual interest rate of9%. If Jack repays$1,500 per year then how long (to the nearest year) will it take him to repay the loan?

• What is the present value of a perpetuity of $100if the appropriate discount rate is7%? If interest rates in general were to double and the appropriate discount rate rose to 14%, what would happen to the present value of the perpetuity?

• Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR (Nominal Interest Rate) is stated to be 18.00%, with interest compounded monthly, what is the card's EFF%?

• When Jane and Patrick Baker were "house hunting" five years ago, the fixed rate on a 30- year mortgage was 6% APR (Nominal Interest Rate) with monthly compounding. After walking through many homes, they finally reached a consensus and decided to buy a $500,000 home. The couple decided to put 20% down payment and took the 30-year mortgage with monthly payments.

• What is Jane and Patrick's monthly mortgage payment?
• Construct an amortization schedule in excel for the loan.
• During the first 5 years, how much has the couple paid towards the mortgage?
• What proportion of this was applied toward interest? What is the balance on their loan today?