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Homework answers / question archive / 1) One year ago you borrowed $10,000 at an annual interest rate of 9 percent to be repaid in thirty-six equal monthly installment a
1) One year ago you borrowed $10,000 at an annual interest rate of 9 percent to be repaid in thirty-six equal monthly installment a. What is your monthly payment? b. Without the use of a loan amortization schedule, what is the current balance on the loan? (Hint: What is the relationship between the present value of the remaining payments to be made on the loan and its current balance?) c. What will be the balance owed on the loan one year from now if all payments are made as scheduled? d. What is the dollar amount of interest to be paid on the loan in the coming year? (Hint: The answers to b and c are very useful in answering d.)
2)Problem 2 (12 marks) SAGE Enterprises just paid a dividend of $2 per share. The current market price is $50 per share. Dividends are expected to grow at a constant rate "g". The risk-free rate is equal to 3% and the share risk premium is equal to 5%. a. Calculate the growth rate of dividends "g". b. Estimate the price of the share 5 years from today.
Problem 5 (12 marks) Consider a company that just paid a dividend a $3 per share. The dividends are expected to grow at the rate of 8% per year for the next 3 years and then at 4% thereafter. a. Draw the timeline for the first 6 years. b. Calculate the expected dividends for the next five years.
3)
1- in the federal reserve lowers interest rates so that the risk-free rate becomes zero, then what will be the ratio given by the price of an at the money call divided by the price of an at the money put with 9.5 years to maturity if markets are in equilibrium? Show your work
2- If the one year continuously compounded interest rate is 20, what is the one-year annual interest rate? show your work
Multiple choice:
If after you created the unit trust the only change to the variables used to price the equity was the passing of time, which of the following would be true 3 months after the unit trust was created?
Which are true for the Black-Scholes equation?
The payoff of a short call position is replicated by which?
1)
Use PMT function in EXCEL to find the monthly payment.
=PMT(rate,nper,pv,fv,type)
rate=9%/12=0.75%
nper=36 months
pv=10000
fv=0
=PMT(0.75%,36,-10000,0,0)=$318.0
Monthly payment=$318.0
b. Please find the amortization schedule with formulas given
| Periods | Opening Balance | Monthly fixed payment | Interest amount=(Opening Balance*0.75%) | Principal amount=Interest payment-Interest | Ending Balance=Opening Balance-Principal |
| 1 | 10000.00 | 318.00 | 75.00 | 243.00 | 9757.00 |
| 2 | 9757.00 | 318.00 | 73.18 | 244.82 | 9512.18 |
| 3 | 9512.18 | 318.00 | 71.34 | 246.66 | 9265.53 |
| 4 | 9265.53 | 318.00 | 69.49 | 248.51 | 9017.02 |
| 5 | 9017.02 | 318.00 | 67.63 | 250.37 | 8766.65 |
| 6 | 8766.65 | 318.00 | 65.75 | 252.25 | 8514.40 |
| 7 | 8514.40 | 318.00 | 63.86 | 254.14 | 8260.26 |
| 8 | 8260.26 | 318.00 | 61.95 | 256.05 | 8004.22 |
| 9 | 8004.22 | 318.00 | 60.03 | 257.97 | 7746.25 |
| 10 | 7746.25 | 318.00 | 58.10 | 259.90 | 7486.35 |
| 11 | 7486.35 | 318.00 | 56.15 | 261.85 | 7224.50 |
| 12 | 7224.50 | 318.00 | 54.18 | 263.81 | 6960.69 |
| 13 | 6960.69 | 318.00 | 52.21 | 265.79 | 6694.90 |
| 14 | 6694.90 | 318.00 | 50.21 | 267.79 | 6427.11 |
| 15 | 6427.11 | 318.00 | 48.20 | 269.79 | 6157.32 |
| 16 | 6157.32 | 318.00 | 46.18 | 271.82 | 5885.50 |
| 17 | 5885.50 | 318.00 | 44.14 | 273.86 | 5611.64 |
| 18 | 5611.64 | 318.00 | 42.09 | 275.91 | 5335.73 |
| 19 | 5335.73 | 318.00 | 40.02 | 277.98 | 5057.76 |
| 20 | 5057.76 | 318.00 | 37.93 | 280.06 | 4777.69 |
| 21 | 4777.69 | 318.00 | 35.83 | 282.16 | 4495.53 |
| 22 | 4495.53 | 318.00 | 33.72 | 284.28 | 4211.25 |
| 23 | 4211.25 | 318.00 | 31.58 | 286.41 | 3924.83 |
| 24 | 3924.83 | 318.00 | 29.44 | 288.56 | 3636.27 |
| 25 | 3636.27 | 318.00 | 27.27 | 290.73 | 3345.55 |
| 26 | 3345.55 | 318.00 | 25.09 | 292.91 | 3052.64 |
| 27 | 3052.64 | 318.00 | 22.89 | 295.10 | 2757.54 |
| 28 | 2757.54 | 318.00 | 20.68 | 297.32 | 2460.22 |
| 29 | 2460.22 | 318.00 | 18.45 | 299.55 | 2160.68 |
| 30 | 2160.68 | 318.00 | 16.21 | 301.79 | 1858.88 |
| 31 | 1858.88 | 318.00 | 13.94 | 304.06 | 1554.83 |
| 32 | 1554.83 | 318.00 | 11.66 | 306.34 | 1248.49 |
| 33 | 1248.49 | 318.00 | 9.36 | 308.63 | 939.86 |
| 34 | 939.86 | 318.00 | 7.05 | 310.95 | 628.91 |
| 35 | 628.91 | 318.00 | 4.72 | 313.28 | 315.63 |
| 36 | 315.63 | 318.00 | 2.37 | 315.63 | 0.00 |
c. Now already 1 year finished and the amount owed in next year=24 month ending balance=$3636.27
d. We have to add 13 to 24 month interest amount=$491.55
2)
Required rate of return of equity = Risk free rate + Share risk premium
Required rate of return of equity = 3% + 5%
Required rate of return of equity = 8%
Price = Dividend * (1 + growth rate(g)) / (Required rate of return of equity - growth rate(g))
$50 = $2 * (1 + g) / (8% - g)
$50 * (8% - g) = $2 * (1 + g)
$4 - 50 * g = $2 + 2 * g
52 * g = $2
g = 2 / 52
growth rate (g) = 3.8462%
Price of the share in 5 years = Dividend * (1 + g)6 / (Required rate of return of equity - growth rate(g))
Price of the share in 5 years = $2 * (1 + 3.8462%)6 / (8% - 3.8462%)
Price of the share in 5 years = $60.38
2)
Timeline
| Time (Year) | 1 | 2 | 3 | 4 | 5 | 6 |
| Dividend | $3 * (1 + 8%) = $3.24 | $3.24 * (1 + 8%) = $3.50 | $3.50 * (1 + 8%) = $3.78 | $3.78 * (1 + 4%) = $3.93 | $3.93 * (1 + 4%) = $4.09 | $4.09 * (1 + 4%) = $4.25 |
Expected dividend, 1 year from now = Dividend * (1 + growth rate)
Expected dividend, 1 year from now = $3 * (1 + 8%)
Expected dividend, 1 year from now = $3.24
Expected dividend, 2 years from now = Expected dividend, 1 year from now * (1 + growth rate)
Expected dividend, 2 years from now = $3.24 * (1 + 8%)
Expected dividend, 2 years from now = $3.50
Expected dividend, 3 years from now = Expected dividend, 2 years from now * (1 + growth rate)
Expected dividend, 3 years from now = $3.50 * (1 + 8%)
Expected dividend, 3 years from now = $3.78
Expected dividend, 4 years from now = Expected dividend, 3 years from now * (1 + growth rate)
Expected dividend, 4 years from now = $3.78 * (1 + 4%)
Expected dividend, 4 years from now = $3.93
Expected dividend, 5 years from now = Expected dividend, 4 years from now * (1 + growth rate)
Expected dividend, 5 years from now = $3.93 * (1 + 4%)
Expected dividend, 5 years from now = $4.09
Expected dividend, 6 years from now = Expected dividend, 5 years from now * (1 + growth rate)
Expected dividend, 6 years from now = $4.09 * (1 + 4%)
Expected dividend, 6 years from now = $4.25
3)
1. Call option and put option premiums are impacted inversely as interest rates change. However, the impact on option prices is fractional; option pricing is more sensitive to changes in other input parameters, such as underlying price, volatility, time to expiry, and dividend yield.
So it interest rate decreases, call money will decrease and put money will increases. As a whole, ratio given by the price of an at the money call divided by the price of an at the money put will drecrease.
2.
r continuous?=ln(1+r)?
20% = ln(1+r)
1 + r = e to power 20%
1 +r = 1.22
r = .22 or 22%
