Using the data in the following table, calculate (based on expectation hypothesis only) the ‘five-year spot rate’ and ‘one-year forward rate four (4) years from now
1.A bond has the following characteristics:
| Face value | $5,000 |
| Maturity | 3 years |
| Coupon | 6%, paid semi-annually |
| Yield to maturity | 10% |
a) Calculate Macaulay duration of the bond.
b) Calculate this bond’s modified duration.
c) Calculate convexity of the bond.
d) Calculate the dollar price change for this bond assuming its yield to maturity increased by 10 basis points (i.e. from 6% to 6.1%). Identify:
I. Modified duration effect (price change calculated using duration formula)
II. Convexity effect (price change due to convexity).
III. Combined price effect and the new bond price.
2.Australian Treasuries represent a significant holding in Graham’s pension portfolio. You decide to analyse the yield curve for Australian Treasury bonds.
a) Using the data in the following table, calculate (based on expectation hypothesis only) the ‘five-year spot rate’ and ‘one-year forward rate four (4) years from now’ assuming annual compounding (fill in the spaces in the table below). Assume that notes of all maturities, including coupon-paying five-year note are currently trading at par of $1,000. Show calculations (5 marks).
| Australian Treasury notes yield curve data | |||||
| Coupon-paying Notes’ Maturities (Years to maturity) | Yield to Maturity | Calculated Spot Rates | Calculated Forward Rates | ||
| 1 | 5.00 | S1 | 5.00 | 5.00 | |
| 2 | 5.20 | S2 | 5.21 | 1f2 | 5.42 |
| 3 | 6.00 | S3 | 6.05 | 2f3 | 7.75 |
| 4 | 6.50 | S4 | 6.60 | 3f4 | 8.27 |
| 5 | 7.00 | S5 | 4f5 |
b) You are considering the purchase of a zero coupon Treasury note with four (4) years to maturity and a face value of $1,000.
Based on the preceding yield curve analysis, calculate both the expected yield to maturity and the price of the security (assuming annual compounding) of such a bond. Show calculations (3 marks).
3. (a)Consider a firm that has just paid a dividend of $2. An analyst expects dividends to grow at a rate of 8% per year for the next five (5) years. After that dividends are expected to grow at a normal rate of 5% per year. Assume that the appropriate discount rate is 7%.
(i) What is the value of the firm’s common stock today?
(ii) What is the price of the stock today if there is no supernormal growth in dividends in the first (5) five years, that is dividends grow at a constant rate of 5% forever?
(b) Tayco Corporation has just paid dividends of $3 per share. The earnings per share for the company was $4. If you believe that the appropriate discount rate is 15% and the long term growth rate in dividends is 6%, and earnings is 6%, what is the firm’s price-earnings (P/E) ratio?.
