FINA 1310_GHI Problem Set 1
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FINA 1310_GHI Problem Set 1
Deadline for Submission: 11:59pm on March 17
Submission Method: upload to the course Moodle
Submissions after the deadline above will NOT be accepted and students will get zero points for the exercise.
There are 10 questions, each question carries 10 points. The total point of the problem set is 100. For each question, you have to write down the formula you use and the final answer to get the points. Do NOT just write down the final answer. Each group needs to submit one copy only (with all answers in a single pdf file). Do not forget to indicate your name, email, UID, and subclass clearly on the cover page of the assignment.
Workings should be submitted for all questions requiring calculations. Please round off all answers to 2 decimal places (the percentage terms should be in the format of 00.00%).
In all of the questions below, all the rate terms such as “interest rate,” “return” and “yield-to- maturity” are annualized (i.e. APR) unless specified otherwise.
Q.1 You want to save money so that you will have $1 million 40 years from now.
a) If you start making your first deposit one month from now, and save the same dollar amount every month from then on, how much do you have to save each month if you earn an interest rate of 10.2%?
b) How much do you have to save each month if you begin the first monthly deposit 10 years from now?
c) How much do you have to save each month if you begin the first monthly deposit one month from now but only make deposits for 30 years?
d) Assume 40 years has passed and you now have $1 million in hand. You retire and
start to withdraw money at the beginning of each month (thus the first withdrawal will be today). You expect that you can live for another 50 years and you would like towithdraw a same dollar amount each month. How much you can withdraw each month if the interest rate is 6% that time?
e) All else the same as in part (d), assume that you would like to have your withdrawal increasing by 0.2% per month. How much you can withdraw in the final month?
Q.2 A bank is designing a two-year loan contract with $50,000 principal. It would like to charge an effective annual rate of 12% with quarterly payments.
a) If the contract requires fixed principal payment, how would the amortization table
look like? Please use the following template and fill the table accordingly (no need to fill in the two grey cells).
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Period |
Beginning Balance |
Payment per Period |
Interest Payment |
Principal Payment |
Ending Balance |
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1 |
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2 |
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… |
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Totals: |
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b) If the contract requires fixed equal payment, how would the amortization table look like?
Q.3 You want to buy a new car for $84,500, using a 5-year loan with quoted interest rate of 4.8% and monthly fixed equal payment.
a) What is your monthly payment?
b) What is the effective annual rate on this loan?
c) After two years of payments, you decide to sell this car and end the loan contract early with a lump-sum payment. How large this lump-sum payment should be?
Q.4 An insurance company sells a perpetuity contract that pays $1,500 monthly, with the first payment starting 10 years (i.e., at month 120, assume today is month 0) from now. The interest rate is 9%.
(a) What should be the market value of this contract today?
(b) Assume all else the same as part (a), but the payment increases by 0.1% per month, and the first payment is $1,500. What should be the market value of this contract today?
(c) [OPTIONAL] Assume all else the same as part (b), but we do not know the interest rate. Instead, we find the market value of this contract to be $150,000. What is the interest rate suggested by this price? (Hint: use the trial-and-error method and please report the APR.)
Q.5 A company issued a 25-year bonds two years ago at a coupon rate of 5.6 percent. The bonds make semi-annual payments. The bond currently sells for 97 percent of its par value.
(a) What is the bond yield-to-maturity? (Hint: please report the APR)
(b) Assume two years from now the bond sells for 105 percent of its par value. What is the bond yield-to-maturity at that time? (Hint: please report the APR)
(c) If an investor buys this bond today and sells it two years from now, what is the investor’s holding period return? (Hint: please report the APR)
Q.6 Company Alpha has a bond outstanding with a coupon rate of 2.9 percent paid semi-annually and 16 years to maturity. The yield to maturity on this bond is 2.7 percent, and the bond has a par value of $5,000.
(a) What is the price of the bond today?
(b) What is the interest rate risk of this bond? (Hint: calculate by what percentage the bond price changes when the interest rate increases by 1 percentage point.)
(c) Company Beta has a similar outstanding bond, except that Company Beta’s bond has a 3.5% coupon rate. Which company’s bond has a higher interest rate risk? How large is the interest rate risk for Company Beta’s bond?
(d) Company Gamma also has a similar outstanding bond, except that Company
Gamma’s bond has a $1,000 face value. Which company’s bond has a higher interest rate risk? How large is the interest rate risk for Company Gamma’s bond?
Q.7 A corporation has just paid a dividend of $2.95 on its stock (thus the first dividend that the current investor can receive will be the next period’s). What is the current share price if:
(a) the growth rate in dividends is expected to be a constant 3.4 percent per year
indefinitely. Investors require a return of 15 percent for the first three years, a return of 13 percent for the next three years, and a return of 11 percent thereafter.
(b) the required return is the same as in part (a), but the dividend growth rate is 5 percent for five years. After that, the dividend growth rate will reduce to 3 percent and last forever.
Q.8 A company is growing quickly. Its dividends are expected to grow at a rate of 30 percent every year for the next three years, with the growth rate falling off to a constant 4 percent thereafter. The required return for the stock is 10 percent (for all years), what is the current share price if:
(a) the company has just paid a dividend of $2.65 (thus the first dividend that the current investor can receive will be the next period’s)?
(b) the first dividend of $2.65 to the current investor will be paid today?
Q.9 Consider a five-year loan of $50,000 with monthly fixed equal payments. The quoted interest rate is 6%.
(a) If the bank charges interest using reducing balance basis, what is the monthly payment? What is the effective annual rate?
(b) If the bank charges interest using flat basis, what is the monthly payment? What is the effective annual rate?
(c) If the bank charges interest using annual rest basis, what is the monthly payment? What is the effective annual rate?
Q.10 Bond X offers 4% coupon with annual payments and had a YTM of 6% five years ago when you bought it. At that time, it had 15 years to maturity. Suppose that now the YTM increases to 10% and you decide to sell Bond X.
(a) What is your nominal holding period return from holding Bond X?
(b) What is your real holding period return if the consumer price index increases from 100 to 150 over these five years?
2024-03-16