2. You are now considering adding a corporate bond to your investment portfolio. The bond was issued last year to have 10 years to maturity (so it has 9 years remaining to maturity from today) The bond has an 8% coupon, and was sold at par ($1,000) when it was issued last year. As the market interest rates went up over the last year, the bond’s current price has fallen to $901.40.
(A). What is the YTM now?
(B). If the market interest rate remains unchanged from today until the end of this year, what will be the bond price at the end of this year?
Note: The price of the bond is determined by the future cash flows to be received from the end of this year.
(C). For the coming year (from today to the end of the this year), what would be the expected current yield and capital gain yield?
To calculate the YTM (yield to maturity) of the bond, we can use the following formula:
YTM = (Annual Interest Payment + (Par Value - Current Bond Price) / Number of Years) / ((Par Value + Current Bond Price) / 2)
Using the given information, we can calculate the YTM:
(A). YTM = (80 + (1,000 - 901.40) / 9) / ((1,000 + 901.40) / 2)
YTM = (80 + 98.6) / (1,450 / 2)
YTM = 178.6 / 725
YTM ≈ 0.2464 or 24.64%
(B). If the market interest rate remains unchanged until the end of this year, the bond price at the end of this year can be calculated using the formula:
Bond Price = Annual Interest Payment / (1 + Market Interest Rate) + (Annual Interest Payment + Par Value) / (1 + Market Interest Rate)^n
Assuming the market interest rate remains unchanged at 8%, we substitute the values into the formula:
Bond Price = 80 / (1 + 0.08) + (80 + 1,000) / (1 + 0.08)^9
Bond Price = 80 / 1.08 + 1,080 / 1.08^9
Bond Price = 74.07 + 635.53
Bond Price ≈ $709.60
Therefore, the bond price at the end of this year would be approximately $709.60.
(C). The current yield and capital gain yield for the coming year can be calculated as follows:
Current yield = Annual Interest Payment / Current Bond Price
Current yield = 80 / 901.40
Current yield ≈ 0.0887 or 8.87%
Capital gain yield = (Ending Bond Price - Beginning Bond Price) / Beginning Bond Price
Capital gain yield = (709.60 - 901.40) / 901.40
Capital gain yield ≈ -0.2128 or -21.28%
Therefore, the expected current yield for the coming year is approximately 8.87%, and the expected capital gain yield for the coming year is approximately -21.28%.
A. To calculate the Yield to Maturity (YTM) of the bond, we need to find the discount rate that equates the present value of all future cash flows from the bond to its current price.
The bond has 9 years remaining to maturity and pays an annual coupon of 8% on a face value of $1,000. The coupon payment can be calculated as follows:
Coupon Payment = Coupon Rate x Face Value
Coupon Payment = 8% x $1,000 = $80
To find the YTM, we need to find the discount rate that makes the present value of future cash flows equal to the current price of $901.40. We also need to take into account that the bond will mature at par value ($1,000) in 9 years.
Using a financial calculator or spreadsheet, you can use the formula:
YTM = [Coupon Payment + (Par Value - Current Price) / Number of Years] / [(Par Value + Current Price) / 2]
Substituting the known values into the equation, we find:
YTM = [($80 + ($1,000 - $901.40) / 9] / [($1,000 + $901.40) / 2]
= [$80 + $9.60] / [$1,450.70 / 2]
≈ $89.60 / $725.35
Therefore, the Yield to Maturity (YTM) of the bond now is approximately 12.36%.
B. If the market interest rate remains unchanged from today until the end of this year, the bond price at the end of this year will depend on the future cash flows. Specifically, it will depend on the coupon payment and the return of the bond to par value at maturity.
Since the bond's yield to maturity is 12.36%, we can assume that it will continue to be the discount rate, unless the market interest rates change. Assuming that the bond's coupon payment remains constant at $80 per year, and the bond matures at its face value of $1,000 in 9 years, we can calculate the bond price using the formula for the present value of an ordinary annuity and the present value of a future lump sum:
Bond Price = Present value of coupon payments + Present value of par value
Present value of coupon payments = Coupon Payment x [(1 - (1 + r)^(-n)) / r]
Present value of par value = Par Value / (1 + r)^n
Where r is the yield to maturity (12.36%), n is the number of years remaining until maturity (9), and the Coupon Payment is $80.
Plugging in the values, we get:
Present value of coupon payments = $80 x [(1 - (1.1236)^(-9)) / 0.1236]
≈ $80 x (1 - 0.3036) / 0.1236
≈ $80 x 0.6964 / 0.1236
≈ $449.49
Present value of par value = $1,000 / (1 + 0.1236)^9
≈ $1,000 / 1.7761
≈ $562.97
Bond Price = Present value of coupon payments + Present value of par value
= $449.49 + $562.97
≈ $1,012.46
Therefore, if the market interest rate remains unchanged from today until the end of this year, the bond price at the end of this year should be approximately $1,012.46.
C. The current yield and capital gain yield for the coming year (from today to the end of this year) can be calculated as follows:
Current Yield = Annual Coupon Payment / Current Price
Using the bond's annual coupon payment of $80 and the current price of $901.40, we can calculate the current yield:
Current Yield = $80 / $901.40
≈ 0.0886 or 8.86%
The current yield represents the annual income (coupon payment) as a percentage of the bond's current price.
Capital Gain Yield = (Price at the End of the Year - Current Price) / Current Price
Using the bond's price at the end of the year of $1,012.46 and the current price of $901.40, we can calculate the capital gain yield:
Capital Gain Yield = ($1,012.46 - $901.40) / $901.40
≈ 0.1233 or 12.33%
The capital gain yield represents the percentage increase in price from the current price to the price at the end of the year.
Therefore, for the coming year, the expected current yield is approximately 8.86% and the capital gain yield is approximately 12.33%.