Zero Coupon Bond
Mid Term – October 2014
Bond Pricing
Qu 1:
Time to Maturity Zero Coupon Rate Discount Factor
1 5% 2 6% 3 7% 4 8% 5 9% Give the formula for the discount factor in terms of the zero coupon rate. Use the formula to fill in the discount factors in the table above (you can write the formula or using excel calculate the numerical value).
Assume that the government wishes to issue a new 5 year bond priced at 100 (called a par coupon bond as it is priced at par i.e. the price is the same as the face value) given the current rates in the above table what coupon will the bond have? If you don’t have excel given the answer in terms of the formula that you needed to fill the above table.
You are advised to make use of the upward sloping yield curve by taking a one year rolling loan and investing at the five year rate. What are the risks of following this strategy? Bond Duration
Qu 2:
What is the Macaulay duration of a zero coupon bond maturing at time T? The Macaulay duration of a perpetual bond with yield y is given by (1+y)/y.
Consider a bond portfolio consisting of 2 bonds where the proportion of assets in bond i (i=1,2) is given by wi so total portfolio is P = w1 P1+w2 P2. Given the Macaulay Duration of bond I (i=1,2) is given by Di what is the duration of the portfolio?
You have a portfolio of 500,000 Rs invested in a perpetual bond paying 10% and 500,000 Rs in a zero coupon bond maturing in 5 years?
Stock Valuation
Qu 3:
Minor Motors stock sells for 200 Rs per share and next year’s dividend is 8.5 Rs.
a. Security analysts are forecasting earnings growth of 7.5% per year for the next five years. Assume that earnings and dividends are expected to grow at 7.5% in perpetuity. What rate of return are investors expecting?
b. Assume instead that Minor Motors generates a Return on Equity of 10% and that its payout ratio is 40% what is the current book value of Minor Motors? What is the growth rate? If investor expect the return calculated in part (a) what
Bond Pricing
Qu 1:
Time to Maturity Zero Coupon Rate Discount Factor
1 5% 2 6% 3 7% 4 8% 5 9% Give the formula for the discount factor in terms of the zero coupon rate. Use the formula to fill in the discount factors in the table above (you can write the formula or using excel calculate the numerical value).
Assume that the government wishes to issue a new 5 year bond priced at 100 (called a par coupon bond as it is priced at par i.e. the price is the same as the face value) given the current rates in the above table what coupon will the bond have? If you don’t have excel given the answer in terms of the formula that you needed to fill the above table.
You are advised to make use of the upward sloping yield curve by taking a one year rolling loan and investing at the five year rate. What are the risks of following this strategy? Bond Duration
Qu 2:
What is the Macaulay duration of a zero coupon bond maturing at time T? The Macaulay duration of a perpetual bond with yield y is given by (1+y)/y.
Consider a bond portfolio consisting of 2 bonds where the proportion of assets in bond i (i=1,2) is given by wi so total portfolio is P = w1 P1+w2 P2. Given the Macaulay Duration of bond I (i=1,2) is given by Di what is the duration of the portfolio?
You have a portfolio of 500,000 Rs invested in a perpetual bond paying 10% and 500,000 Rs in a zero coupon bond maturing in 5 years?
Stock Valuation
Qu 3:
Minor Motors stock sells for 200 Rs per share and next year’s dividend is 8.5 Rs.
a. Security analysts are forecasting earnings growth of 7.5% per year for the next five years. Assume that earnings and dividends are expected to grow at 7.5% in perpetuity. What rate of return are investors expecting?
b. Assume instead that Minor Motors generates a Return on Equity of 10% and that its payout ratio is 40% what is the current book value of Minor Motors? What is the growth rate? If investor expect the return calculated in part (a) what