O'Brien Ltd.'s outstanding bonds have a $1,000 par value, and they mature in 25 years. Their nominal annual, not semiannual yiel
d to maturity is 9.25%, they pay interest semiannually, and they sell at a price of $875. What is the bond's nominal coupon interest rate?
1 answer:
Answer:
7.84%
Explanation:
Given:
Bond's par value (FV) = $1,000
Maturity (nper) = 25 × 2 = 50 periods (since it's semi-annual)
YTM (rate) = 0.0925÷2 = 0.04625 semi annually
Price of bond (PV) = $875
Calculate coupon payment (pmt) using spreadsheet function =pmt(rate,nper,-PV,FV)
PV is negative as it's a cash outflow.
So semi- annual coupon payment is $39.20
Annual coupon payment = 39.2×2 = $78.40
Nominal Coupon rate = Annual coupon payment ÷ Par value
= 78.4 ÷ 1000
= 0.0784 or 7.84%
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Answer:
Real return on investment: 22.9465%
Explanation:
Okay let's explain each concept we have given:
<em>Face Value</em> $1,000
This is the ammount Lambert will pay at maturity
Purchase Value $ 960
This is the Ammount we pay for the bond
<em>Market Value of the bond today $ ???</em>
This is what we need to determinate to see the return we got
Once we got the market Value we will do:
Market Value / Purchase Value - 1 = rate of return
Now the <em>market value today will be the present value of the bond,</em> and the bond has the following data:
- Mature in 14 year
- bond rate 7% annualy.
So each year we receive the 7% of the face value ($1,000) = $70
And at the end of the bond life we receive 1,000
We need to bring this numbers at present day using the real market rate, because the economy is having inflation:
market rate 8%
inflation rate 2.7%
real rate:
(1+rate)/(1+inflation) -1 = real rate
real rate = 5.16%
To know the present value of the bond we will have to consider:
- present value of an annuity of 70$ during 14 year at a rate of 5.16% =
- present value of the 1,000 that will be pay at maturity at a rate of 5.16%
<em>The annuity will be </em>
$685,87
<em>The present value of the 1,000 will be</em>
face value/(1+rate)^time
1,000/(1+0.0516)^14 = $494,42
for a total of $1.180,29
Now we will calculate the real return on the investment:
we receive 1.180,29 for 960 so the rate is
1.180,29 /960 - 1 = 0.229465 = 22.9465%