Questions: Sub-Annual Time Value of Money
1. A zero-coupon bond is a security that pays no interestand is therefore bought at a substantial discount from its face value. If stated interest rates are 5% annually (with monthly compounding) how much would you pay today for a zero-coupon bond with a face value of $1,900 that matures in 8 years? Please round your answer to the nearest cent.
2. A financial institution offers a "double-your-money" savings account in which you will have $2 in 7 years for every dollar you invest today. What stated annual interest rate (assuming monthly compounding) does this account offer?
Please specify your answer in decimal terms and round your answer to the nearest thousandth (e.g., enter 12.3 percent as 0.123).
3. You have $50,000 in savings for retirement in an investment earning a stated annual rate of 5% compounded semi-annually. You aspire to have $1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal? Please round your answer to the nearest hundredth. Note that the HP 12c financial calculator rounds up the periods result to the next integer and will not give the correct answer to the nearest hundredth. Therefore, you should use Excel or a financial calculator that does provide decimal precision to the number of periods.
4. You deposit $1,200 in a bank account that pays 9% stated annual interest compounded semi-annually. What is the value of your investment at the end of 4 years? Please round your answer to the nearest cent.
Net Present Value
1. A firm that purchases electricity from the local utility for $350,000 per year is considering installing a steam generator at a cost of $270,000. The cost of operating this generator would be $270,000 per year, and the generator will last for five years. If the firm buys the generator, it does not need to purchase any electricity from the local utility. The cost of capital is 13%. For the local utility option, consider five years of electricity purchases. For the generator option, assume immediate installation, with purchase and operating costs in the current year and operating costs continuing for the next four years. Assume payments under both options at the start of each year (i.e., immediate, one year from now, four years from now). What is the net present value of the more attractive choice? Please round your answer to the nearest dollar. Report the NPV of cost as a negative number.
2. A firm that purchases electricity from the local utility is considering installing a steam generator. A large generator costs $280,000 whereas a small generator costs $140,000. The cost of operating the generator would be $200,000 per year for the large and $220,000 for the small. Either generator will last for five years. The cost of capital is 9%. For each generator option, assume immediate installation, with purchase and operating costs in the current year and operating costs continuing for the next four years. Assume payments under both options at the start of each year (i.e., immediate, one year from now, four years from now). What is the net present value of the more attractive generator? Please round your answer to the nearest dollar. Report the NPV of cost as a negative number.
3. A prospective MBA student earns $45,000 per year in her current job and expects that amount to increase by 6% per year. She is considering leaving her job to attend business school for two years at a cost of $30,000 per year. She has been told that her starting salary after business school is likely to be $90,000 and that amount will increase by 16% per year. Consider a time horizon of 10 years, use a discount rate of 9%, and ignore all considerations not explicitly mentioned here. Assume all cash flows occur at the start of each year (i.e., immediate, one year from now, two years from now, nine years from now). Also assume that the choice can be implemented immediately so that for the MBA alternative the current year is the first year of business school. What is the net present value of the more attractive choice? Please round your answer to the nearest dollar.
Growing Annuity/Perpetuity
1. What is the present value of a series of payments received each year for 9 years, starting with $300 paid one year from now and the payment growing in each subsequent year by 3%? Assume a discount rate of 5%. Please round your answer to the nearest cent.
2. What is the present value of a series of payments received each year for 5 years, starting with $200 paid one year from now and the payment growing in each subsequent year by 1%? Assume a discount rate of 2%. Please round your answer to the nearest cent.
3. What is the present value of a series of payments received each year forever, starting with $500 paid one year from now and the payment growing in each subsequent year by 2%? Assume a discount rate of 5%. Please round your answer to the nearest cent.
4. What is the present value of a series of payments received each year forever, starting with $300 paid one year from now and the payment growing in each subsequent year by 10%? Assume a discount rate of 12%. Please round your answer to the nearest cent.
Constant Annuity/Perpetuity
1. What is the present value of an annuity in which $400 is paid each year for 9 years, assuming a discount rate of 7% and the first payment is received one year from now? Please round your answer to the nearest cent.
2. What is the present value of an annuity in which $500 is paid each year for 6 years, assuming a discount rate of 8% and the first payment is received one year from now? Please round your answer to the nearest cent.
3. What is the present value of $400 paid each year forever, assuming a discount rate of 11% and the first payment is received one year from now? Please round your answer to the nearest cent.
4. What is the present value of $500 paid each year forever, assuming a discount rate of 8% and the first payment is received one year from now? Please round your answer to the nearest cent.
Bond
1. What is the current value of a zero-coupon bond that pays a face value of $1,000 at maturity in 11 years if the appropriate discount rate is 12%. Please round your answer to the nearest cent.
2. What interest rate is implicit in a $1,000 par value zero-coupon bond that matures in 6 years if the current price is $580. Please specify your answer in decimal terms and round your answer to the nearest thousandth (e.g., enter 12.3 percent as 0.123).
3. What is the current value of a $1,000 bond with a 9% annual coupon rate (paid annually) that matures in 10 years if the appropriate discount rate is 6%. Please round your answer to the nearest cent.
4. What is the current value of a $1,000 bond with a 8% annual coupon rate (paid semi-annually) that matures in 9 years if the appropriate stated annual discount rate is 5%. Please round your answer to the nearest cent.