Gabriele Enterprises has bonds on the market making annual payments, with eight years to maturity, a par value of $1,000, and se
lling for $948. At this price, the bonds yield 5.1 percent. What must the coupon rate be on the bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
1 answer:
Answer:
Coupon rate = 0.04292 or 4.292%
Explanation:
To calculate the coupon rate of the bond, we will, use the formula for the price of the bond. As the bond is an annual bond, the coupon payment, number of periods and semi annual YTM will be,
Coupon Payment (C) = x
Total periods (n)= 8
r or YTM = 0.051 or 5.1%
The formula to calculate the price of the bonds today is attached.
948 = x * [( 1 - (1+0.051)^-8) / 0.051] + 1000 / (1+0.051)^8
948 = x * 6.437166243 + 671.7045216
948 - 671.7045216 = x * 6.437166243
276.2954784 / 6.437166243 = x
x = $42.92191128 rounded off to $42.92
Thus, the coupon payment on bond is $42.92
As the coupon payment is calculated by multiplying the coupon rate with the face value of the bond, then the coupon rate will be:
Coupon payment = face value * coupon rate
42.92 = 1000 * Coupon rate
Coupon rate = 42.92 / 1000
Coupon rate = 0.04292 or 4.292%
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Explanation:
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If collect now, the price for each bushel is $27
As the price per bushel decrease by $1.50 per bushel each week
=> After x weeks, the price of a bushel decrease: 1.5x ($)
=> The price of 1 bushel after x weeks is: 27 - 1.5x ($)
If collect now, each tree can yield 7 bushels
As the yield increases by half a bushel per week for the next 5 weeks
=> After x weeks with x ≤ 5, each trees would yields: 7 + 0.5x (bushels)
The return = The price of each bushes × The quantity of bushels
=>
⇔
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We have: if the equation has the form of with a≠0, its maximum value is:
In the equation , we have: a = -0.75; b = 3; c = 189
=>
To look for the number of weeks, we should find x (0≤x≤5) with which y = 192
⇔
⇔
⇔
⇔
⇔
⇔ x = 2
The oranges should be picked in 2 weeks for maximum return