week 3 Problems - Problem #3, Lycan, Inc. has 7 percent...

week 3 Problems
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Problem #3, Lycan, Inc. has 7 percent coupon bonds on the market that have 8 years left to maturity. The bonds make annual payment. If the YTM on these bonds is 9 percent, what is the current bond price? The price any is any bond is the PV of the interest, Plus the PV of the par value. The problem assumes an annual coupon. The price of the bond will be: P=$70({1-[1/(1+0.07)]8}/.09)+$1,000[1/(1+.09)8] P=2302.066 We would like to introduce shorthand notation here. Rather than write ( or type, as the case may be ) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equation as: PVIFAR, t= ({1-1[1/(1+r)]t}/r) Which stands for Present Value Interest Factor of an Annuity? These abbreviation are shorthand notation for the equation in which the interest rate and the number of period are substituted into the equation and solved. We will use this shorthand notation in the remainder of the solution key. The bond price equation for this problem would be: P=$70(PVIFA7%, 8) + $1,000(PVIF7%, 8) P=$889.30 #5, Coupon Rates. Merton Enterprises has bonds on the market making annual payment, with 16 years to maturity, and selling for $963. At this price, the bonds yield 7.5 percent. What must the coupon rate be on Merton’s bonds? Here we need to find the coupon the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P=$963= C x(PVIFA7.5%, 16)+$1,000x (PVIF7.5%.16)
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