Setrakian Industries needs to raise $51.1 million to fund a new project. The com

Question

Setrakian Industries needs to raise $51.1 million to fund a new project. The company will sell bonds that have a coupon rate of 5.87 percent paid semiannually and that mature in 20 years. The bonds will be sold at an initial YTM of 6.19 percent and have a par value of $2,000. How many bonds must be sold to raise the necessary funds? (Round your intermediate calculations to two decimal places and final answer to the nearest whole number.)

51,100 bonds

25,550 bonds

26,516 bonds

33,145 bonds

80,810 bonds

Explanation / Answer

26,516 bonds

Working:

Step-1:Calculation of current price of bond Current Price of bond is the present value of cash flow from bond. Present Value of coupon Interest $ 1,336.24 Present Value of Par Value $ 590.92 Current Price $ 1,927.16 Working: # 1 Semi-annual interest = Par Value x Semi annual coupon rate = $ 2,000.00 x 5.87% x 6/12 = $ 58.70 # 2 Present value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.03095)^-40)/0.03095 i 6.19%/2 = 0.03095 =                 22.76387 n 20*2 = 40 # 3 Present Value of 1 = (1+i)^-n = (1+0.03095)^-40 =                   0.29546 # 4 Present value of coupon interest = $       58.70 x 22.76387 = $ 1,336.24 Present value of Par Value = $ 2,000.00 x     0.29546 = $     590.92 Step-2:Calculation of number of bonds issued Number of bonds issued = Total funds needed/Current Price of one bond = $       5,11,00,000 / $ 1,927.16 =                     26,516 Bonds Thus, Number of bonds needed to raise fund 26,516 Bonds

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