Please use excel functions to do the calculations on the worksheet for full credit! Note that there is more than one tab in this spreadsheet.Problemset1.xlsx
Please use excel functions to do the calculations on the worksheet for full credit! Note that there is more than one tab in this spreadsheet.
future value
| What would the future value of $100 be after 5 years at 10% compound interest? | |||
| N | 5 | ||
| I | 10% | ||
| PV | $100 | ||
| PMT | $0 | FV= | |
| Suppose you currently have $2,000 and plan to purchase a 3-year certificate of deposit (CD) that pays 4% interest compounded annually. How much will you have when the CD matures? | |||
| N | 3 | ||
| I | 4% | ||
| PV | $2,000 | ||
| PMT | $0 | FV= | |
| A company’s sales in 2009 were $100 million. If sales grow at 8%, what will they be 10 years later? | |||
| N | 10 | ||
| I | 8% | ||
| PV ($M) | $100 | ||
| PMT | $0 | FV ($M)= | |
| How much would $1, growing at 5% per year, be worth after 100 years? | |||
| N | 100 | ||
| I | 5% | ||
| PV | $1 | ||
| PMT | $0 | FV= | |
| What would FV be if the growth rate were 10%? | |||
| N | 100 | ||
| I | 10% | ||
| PV | $1 | ||
| PMT | $0 | FV= | |
present value
| Suppose a risk-free bond promises to pay $2,249.73 in 3 years. If the going risk-free interest rate is 4%, how much is the bond worth today? | |||
| N | 3 | ||
| I | 4% | ||
| PMT | $0 | ||
| FV | $2,249.73 | PV= | |
| How would your answer change if the bond matured in 5 rather than 3 years? | |||
| N | 5 | ||
| I | 4% | ||
| PMT | $0 | ||
| FV | $2,249.73 | PV= | |
| If the risk-free interest rate is 6% rather than 4%, how much is the 5-year bond worth today? | |||
| N | 5 | ||
| I | 6% | ||
| PMT | $0 | ||
| FV | $2,249.73 | PV= | |
Interest rate
| Suppose you can buy a U.S. Treasury bond which makes no payments until the bond matures 10 years from now, at which time it will pay you $1,000. What interest rate would you earn if you bought this bond for $585.43? | |||
| N | 10 | ||
| PMT | $0 | ||
| PV | $585.43 | ||
| FV | $1,000 | I = | |
| What rate would you earn if you could buy the bond for $550? | |||
| N | 10 | ||
| PMT | $0 | ||
| PV | $550.00 | ||
| FV | $1,000 | I = | |
| Microsoft earned $0.33 per share in 1997. Fourteen years later, in 2011, it earned $2.75. What was the growth rate in Microsoft’s earnings per share (EPS) over the 14-year period? | |||
| N | 14 | ||
| PMT | $0 | ||
| PV | $0.33 | ||
| FV | $2.75 | I = | |
| If EPS in 2011 had been $2.00 rather than $2.75 what would the growth rate have been? | |||
| N | 14 | ||
| PMT | $0 | ||
| PV | $0.33 | ||
| FV | $2.00 | I = | |
Perpetuity
| What is the present value of a perpetuity that pays ₤1,000 per year, beginning one year from now, if the appropriate interest rate is 5%? | |||
| PMT | £1,000 | ||
| I | 5% | PV= | |
| What would the value be if the perpetuity began its payments immediately? | |||
| The perpetuity formula values payments 1 through infinity. If a payment is to be received immediately, it must be added to the formula result. | |||
| PMT | £1,000 | ||
| I | 5% | PV= | |
Annuity
| What is the PVA of an ordinary annuity with 10 payments of $100 if the appropriate interest rate is 10%? | ||||
| N | 10 | |||
| I | 10% | |||
| PMT | -$100 | |||
| FV | $0 | PV= | ||
| What would the PVA be if the interest rate were 4%? | ||||
| N | 10 | |||
| I | 4% | |||
| PMT | -$100 | |||
| FV | $0 | PV= | ||
| What would the PVAs be if we were dealing with annuities due? | ||||
| Part a | Part b | |||
| BEGIN MODE | BEGIN MODE | |||
| N | 10 | N | 10 | |
| I | 10% | I | 4% | |
| PMT | -$100 | PMT | -$100 | |
| FV | $0 | FV | $0 | |
| PV | PV | |||
| Assume that you are offered an annuity that pays $100 at the end of each year for 10 years. You could earn 8% on your money in other equally risky investments. What is the most you should pay for the annuity? | ||||
| N | 10 | |||
| I | 8% | |||
| PMT | -$100 | |||
| FV | $0 | PV= | ||
| If the payments began immediately, then how much would the annuity be worth? | ||||
| BEGIN MODE | ||||
| N | 10 | |||
| I | 8% | |||
| PMT | -$100 | |||
| FV | $0 | PV= |
NPV
| What is the present value of a 5-year ordinary annuity of $100 plus an additional $500 at the end of Year 5 if the interest rate is 6%? | ||||||
| Interest rate | 6% | |||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Ann Pmt | $0 | $100 | $100 | $100 | $100 | $100 |
| Lump Sum | $500 | |||||
| Total CFs | $0 | $100 | $100 | $100 | $100 | $600 |
| NPV | ||||||
| What is the present value of the following uneven cash flow stream: $0 at Time 0, $100 at the end of Year 1 (or at Time 1), $200 at the end of Year 2, $0 at the end of Year 3, and $400 at the end of Year 4, assuming the interest rate is 8%? | ||||||
| Interest rate | 8% | |||||
| Year | 0 | 1 | 2 | 3 | 4 | |
| CFs | $0 | $100 | $200 | $0 | $400 | |
| NPV | ||||||
IRR
| An investment costs $465 now and is expected to produce cash flows of $100 at the end of each of the next 4 years, plus an extra lump sum payment of $200 at the end of the 4th year. What is the expected rate of return on this investment? | |||||
| Year | 0 | 1 | 2 | 3 | 4 |
| Ann Pmt | -$465 | $100 | $100 | $100 | $100 |
| Lump Sum | $200 | ||||
| Total CFs | -$465 | $100 | $100 | $100 | $300 |
| IRR | |||||
| An investment costs $465 and is expected to produce cash flows of $100 at the end Year 1, $200 at the end of Year 2, and $300 at the end of Year 3. What is the expected rate of return on this investment? | |||||
| Year | 0 | 1 | 2 | 3 | |
| CFs | -$465 | $100 | $200 | $300 | |
| IRR |
Value of bond
| A bond that matures in six years has a par value of $1,000, an annual coupon payment of $80, and a market interest rate of 9%. What is its price? | ||
| Years to Maturity | 6 | |
| Annual Payment | $80 | |
| Par value | $1,000 | |
| Going rate, rd | 9% | |
| Value of bond = | ||
| Last year a firm issued 30-year, 8% annual coupon bonds at a par value of $1,000. (1) Suppose that one year later the going rate drops to 6%. What is the new price of the bonds, assuming that they now have 29 years to maturity? | ||
| Years to Maturity | 29 | |
| Coupon rate | 8% | |
| Annual Payment | $80 | |
| Par value | $1,000 | |
| Going rate, rd | 6% | |
| Value of bond = |
Yield of bond
| A bond currently sells for $850. It has an eight-year maturity, an annual coupon of $80, and a par value of $1,000. What is its yield to maturity? What is its current yield? | ||||||
| Years to Maturity | 8 | |||||
| Annual Payment | $80.00 | |||||
| Current price | $850.00 | |||||
| Par value = FV | $1,000.00 | |||||
| Going rate, rd =YTM: | ||||||
| Annual Payment | $80.00 | |||||
| Current price | $850.00 | |||||
| Current yield: | ||||||
| A bond currently sells for $1,250. It pays a $110 annual coupon and has a 20-year maturity, but it can be called in 5 years at $1,110. What are its YTM and its YTC? Is it likely to be called if interest rates don't change? | ||||||
| Years to Maturity | 20 | Years to Call | 5 | |||
| Annual Payment | $110 | Annual Payment | $110 | |||
| Current price | $1,250 | Current price | $1,250 | |||
| Par value = FV | $1,000 | Call price | $1,110 | |||
| YTM | YTC | |||||
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