Question
In: Finance
Dominique LeBlanc is the owner of a new ten-year $50,000 8% par-value bond with a Bermuda...
Dominique LeBlanc is the owner of a new ten-year $50,000 8% par-value bond with a Bermuda option and annual coupons. Allowable call dates are at the ends of years 6through 10, and the call premium at the end of year n is $300(10-n). Dominique purchased the bond for $51,975.00.
A) Find the lowest yield that Dominique may receive during the period she holds the bond.
B) Find the highest yield that Dominique may receive during the period she holds the bond.
C) Upon receipt, Dominique deposits each coupon and the redemption amount in an ac-count earning 6%. Find the lowest yield that Dominique may receive during the ten-year period.
D) Upon receipt, Dominique deposits each coupon and the redemption amount in an ac-count earning 6%. Find the highest yield that Dominique may receive during the ten-year period.
Solutions
Expert Solution
| n | A=300*(10-n) | Fv=50000+A | ||||||
| Year | Call Premium | Amount of Receipt after n Years | ||||||
| 6 | 1200 | $51,200 | ||||||
| 7 | 900 | $50,900 | ||||||
| 8 | 600 | $50,600 | ||||||
| 9 | 300 | $50,300 | ||||||
| 10 | 0 | $50,000 | ||||||
| n | Year | 6 | 7 | 8 | 9 | 10 | ||
| Nper | Number of Years | 6 | 7 | 8 | 9 | 10 | ||
| Pmt | Annual Coupon Payment =50000*8% | $4,000 | $4,000 | $4,000 | $4,000 | $4,000 | ||
| Pv | Purchase Price | $51,975 | $51,975 | $51,975 | $51,975 | $51,975 | ||
| Fv | Terminal receipt at end of n years | $51,200 | $50,900 | $50,600 | $50,300 | $50,000 | ||
| RATE | Yield | 7.49% | 7.46% | 7.44% | 7.43% | 7.43% | ||
| (Using RATE function of excel) | ||||||||
| A | LOWEST YIELD | 7.43% | ||||||
| Holding Period=10 Years | ||||||||
| B | HIGHEST YIELD | 7.49% | ||||||
| Holding Period=6 Years | ||||||||
| C | Future Value(FV) at end of 10 years | |||||||
| (Cash Flow)*((1+i)^(10-n)) | ||||||||
| i=interest rate, n=year of cash flow | ||||||||
| Interest rate =i=6%=0.06 | n | A | FV=A*(1.06^(10-n) | B | FV=B*(1.06^(6-n) | |||
| Year | Cash Flow | Future Value | Cash Flow | Future Value | ||||
| 1 | $4,000 | $6,758 | $4,000 | $5,353 | ||||
| 2 | $4,000 | $6,375 | $4,000 | $5,050 | ||||
| 3 | $4,000 | $6,015 | $4,000 | $4,764 | ||||
| 4 | $4,000 | $5,674 | $4,000 | $4,494 | ||||
| 5 | $4,000 | $5,353 | $4,000 | $4,240 | ||||
| 6 | $4,000 | $5,050 | $55,200 | $55,200 | ||||
| 7 | $4,000 | $4,764 | SUM | $79,101 | ||||
| 8 | $4,000 | $4,494 | ||||||
| 9 | $4,000 | $4,240 | ||||||
| 10 | $54,000 | $54,000 | ||||||
| SUM | $102,723 | |||||||
| Yield =R for 10 years | ||||||||
| 51975*(1+R)^10=102723 | ||||||||
| (1+R)^10=102723/51975 | 1.98 | |||||||
| 1+R=1.98^(1/10)= | 1.07 | |||||||
| Yield =R= | 7.05% | |||||||
| Yield =R1 for 6 years | ||||||||
| 51975*(1+R)^10=79101*(1.06^4) | $99,864 | |||||||
| (1+R1)^10=99864/51975 | 1.92 | |||||||
| 1+R1=1.92^(1/10)= | 1.07 | |||||||
| Yield =R= | 6.75% |
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