Respuesta :
The amount of profit or loss on an investment over time is determined by the rate of return (RoR). Calculating the rate of return involves dividing the initial value by the current value and multiplying the result by 100.
"Given"
Face value = $1,00 (P)
Annual coupon payment = $4 (C). So coupon rate = 4%.
Matuirty years = 5 years (n)
Bond price = $90 (price)
a. The following equation can be used to determine this bond's yield to maturity:
Bond price is C(1+r)n + C(1+r)n + C(1+r)n + C+P(1+r)n.
By using the given information and this formula, the following equation can be used to determine this bond's yield to maturity:
Bond price equals $4(1+r)*1, $4(1+r)*2, $4(1+r)*3, $4(1+r)*4, and $104(1+r)*5.
b. The yield until maturity (YTM)
We'll use a calculating process known as trial and error to determine the YTM. The bond is trading at a discount since its price is lower than its par value, and as a result, the yield-to-maturity (YTM) should be higher than the coupon rate (4%). To match the present value of the bond with its price, let's assume a rate of 6% and then change this anticipated rate accordingly.
We will determine the YTM, using the bond price formula as below:
Price of Bond = C(PVIFA, r%,n years)+ P(PVIF, r%,n years)
= $90 = $4 (PVIFA,r%,5) + $100(PVIF,r%.5)
= $90 = $4 (PVIFA,6.39%,5) + $100(PVIF,6.39%,5)
= $90 = $4 *(1-((1+6.39%)^-5)/6.39%) + Face value*(1/(1+6.39%)^5)
= $90 = $4 * 4.168045665 + $100 * 0.733661882
= $90 = 16.67218 + 73.3662
= $90 = $ $90.03838
So here we see that the derived value of $90.04 almost equals the given price of the bond ($90) at an estimated rate of 6.39%.
Hence the YTM = 6.39%.
c. If the bond's price drops from $90 to $85 over the course of a year, its annual rate of return is:
The amount of the payment difference between the bond's initial and revised prices will be taken into account when calculating the rate of return, followed by the amount of the coupon payment received. Over the course of the year, a capital loss was incurred because the bond's price dropped from $90 to $85.
Rate of return = (Current price − initial price ÷ initial price) + (interest amount ÷ initial price)
($85 − $90) ÷ $90 + ($4 ÷$90) = $−5 ÷ $90 + 0.0444
= -0.0556 + 0.0444
= -0.0112
= -1.12%
So bond's rate of return over the year = -1.12%
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