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Mediterranean Hotel Investments PTY LTD, decides to issue 40-year bonds with a face value of $1000 and semiannual coupon payments
Mediterranean Hotel Investments PTY LTD, decides to issue 40-year bonds with a face value of $1000 and semiannual coupon payments. The effective annual yield on other bonds of similar risk and time to maturity is 6.5%, so the company decides to offer 7% annual coupon to attract investors. What would be a fair price for these bonds? Show all workings. Imagine that immediately after issue, the general level of interest rates in the economy moves to such an extent that the value of the Mediterranean Hotel Investments’ bond shifts to exactly $1000. What would now be the new bond-equivalent yield (the one that will be advertised in the financial press as an annual rate and is variously called Nominal Interest Rate, Quoted Interest Rate or sometimes just yield or interest rate)?
Expert Solution
Fair Price of Bond : Fair price of the bond is simply present value of all future cashflow (interest and maturity value) at expected yield i.e. 6.5%. It can be calculated in following manner
Value of bond = Interest * Cumulative PVF for 80 Semi annuals @3.25% + MaturityValue * PVF@3.25%
= (1000*7%*6/12) *28.387 + 1000* 0.0774
= 993.545 + 77.4
= 1070.945
It has been assumed that maturity value is at par.
Since coupon payments are semi annual hence ratebecomes half and time become double. here rate will be 6.50/2 = 3.25 and time will be 40*2 = 80
If value of bond reaches to 1000 , then yield from the bond will be 7% i.e. equivalent to interest rate. At this rate present value of all future cashflows i.e. interest and maturity value.
Value of bond @ 7 %
= Interest * Cumulative PVF@3.50% + MaturityValue * PVF@3.50%
= 35 *26.748 + 1000* 0.06379
= 936.18+63.79
= 999.97 i.e. 1000
Hence yield is 7%
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