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Sam Strother and Shawna Tibbs
Sam Strother and Shawna Tibbs are vice presidents of Mutual of Seattle Insurance Company and co-directors of the company’s pension fund management division. An important new client, the North-Western Municipal Alliance, has requested that Mutual of Seattle present an investment seminar to the mayors of the represented cities, and Strother and Tibbs, who will make the actual presentation, have asked you to help them by answering the following questions.
F1. What is the yield to maturity on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887.00? That sells for $1,134.20? What does the fact that a bond sells at a discount or at a premium tell you about the relationship between and the bond’s coupon rate?
F2. What are the total returns, the current yield, and the capital gains yield for the discount bond? (Assume the bond is held to maturity and the company does not default on the bond.)
Part 2: Create a 3-5-slide PowerPoint presentation in which you summarize your answers from the mini case. Be sure to include graphs, charts, and trends, as appropriate.
Sample Answer
This analysis addresses the bond valuation questions for the investment seminar and outlines the structure for the accompanying presentation.
📊 F1. Bond Yield to Maturity (YTM) Analysis
The Yield to Maturity (YTM) is the internal rate of return (IRR) earned by an investor who buys the bond today at the market price and holds it until maturity. It is the discount rate that equates the present value of the bond's cash flows (coupons and par value) to its current market price.
The Yield to Maturity (YTM) is the internal rate of return (IRR) earned by an investor who buys the bond today at the market price and holds it until maturity.1 It is the discount rate that equates the present value of the bond's cash flows (coupons and par value) to its current market price.2
Current market price (present value, entered as negative)
I/YR (YTM)
$10.91\%$
Calculated YTM
The YTM for the bond selling at 3$\$887.00$ is 4$10.91\%$.5
Case B: Bond Sells at a Premium ($\$1,134.20$)
Variable
Value
Description
N
$10$
Years to maturity
PMT
$\$90$
Annual coupon payment
FV
$\$1,000$
Par value (future value)
PV
$-\$1,134.20$
Current market price (present value, entered as negative)
I/YR (YTM)
$7.08\%$
Calculated YTM
The YTM for the bond selling at $\$1,134.20$ is $7.08\%$.
2. Relationship between Price, Coupon Rate, and YTM
The fact that a bond sells at a discount or a premium tells you the relationship between its coupon rate and its YTM (the market rate of interest for a similar risk bond):
Discount Bond (Price < Par Value): If a bond sells at a discount ($\$887.00 < \$1,000$), its YTM ($10.91\%$) is greater than its Coupon Rate ($9\%$). This happens because the bond's fixed coupon payment is lower than what the current market demands, so the bond must be sold at a lower price to increase the buyer's effective yield.
Premium Bond (Price > Par Value): If a bond sells at a premium ($\$1,134.20 > \$1,000$), its YTM ($7.08\%$) is less than its Coupon Rate ($9\%$). This happens because the bond's fixed coupon payment is higher than the current market rate, making the bond more attractive and allowing it to be sold at a higher price.
💰 F2. Total Returns, Current Yield, and Capital Gains Yield
These calculations assume the investor holds the discount bond (purchased at $\$887.00$) to maturity, and the YTM remains constant at $10.91\%$.