Harpeth Valley Water District has a bond outstanding with a coupon rate of 3.63 percent and semiannual payments. The bond mature
s in 23 years, with a yield to maturity of 4.17 percent, and a par value of $5,000. What is the market price of the bond
1 answer:
Answer:
Market price of Bond = $4603.116669 rounded off to $4603.12
Explanation:
To calculate the price of the bond, we need to first calculate the coupon payment per period. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,
Coupon Payment (C) = 5000 * 0.0363 * 1/2 = $90.75
Total periods (n)= 23 * 2 = 46
r = 4.17% * 1/2 = 2.085% or 0.02085
The formula to calculate the price of the bonds today is attached.
Bond Price = 90.75 * [( 1 - (1+0.02085)^-46) / 0.02085] + 5000 / (1+0.02085)^46
Bond Price = $4603.116669 rounded off to $4603.12
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Model a12 b22 c124
Sales Price per unit 50 100 400
Less: Variable Cost per unit 35 70 300
Contribution Margin per unit 15 30 100
The next step is to calculate the weighted-average contribution margin per unit for the sales mix using the following formula:
Model a12 CM per Unit ×
Model a12 Sales Mix Percentage<span>
+ Model b22 CM per Unit × Model b22 Sales Mix Percentage
+ Model c124 CM per Unit × Model c124 Sales Mix Percentage
<span>= Weighted Average Unit Contribution Margin (WACM)</span></span>
Contribution Margin per unit 15 30 100
X Sales Mix Percentage 60% 15% 25%
WACM 9 4.5 25
Weighted Average Unit Contribution Margin (sum) 38.5
The next step is to find the break-even point using the WACM.
<span> <span><span> <span> Total Fixed Cost </span> <span> $269,500 </span> </span> <span> <span> ÷ Weighted Average CM per Unit </span> <span> $38.50 </span> </span> <span> <span> Break-even Point in Units of Sales Mix </span> <span> 7,000 </span> </span> </span></span>
The next step is to calculate the number of units of each model at break-even point
<span> <span><span> <span> Model </span> <span> a12 </span> <span> b22 </span> <span> c124 </span> </span> <span> <span> Sales Mix Ratio </span> <span> 60% </span> <span> 15% </span> <span> 25% </span> </span> <span> <span> × Total Break-even Units </span> <span> 7,000 </span> <span> 7,000 </span> <span> 7,000 </span> </span> <span> <span> Product Units at Break-even Point </span> <span> 4,200 </span> <span> 1,050 </span> <span> 1,750 </span> </span> </span></span><span> </span>
