Hard Spun Industries (HSI) has a project that it expects will produce a cash flo

Question

Hard Spun Industries (HSI) has a project that it expects will produce a cash flow of $1.8 million in 13 years. To finance the project, the company needs to borrow $1.0 million today. The project will also produce intermediate cash flows of $100,000 per year that HSI can use to service coupon payments of $50,000 every six months. Based on the risk of this investment, market participants will require a 11.0% yield. If HSI wishes a maturity of 13 years (matching the arrival of the lump sum cash flow), what does the face value of the bond have to be? Recall that the compounding interval is 6 months and the YTM, like all interest rates, is reported on an annualized basis.

Explanation / Answer

Here e have:

Price (PV) = 1000,000

Semiannual coupon amount (PMT) = 100,000/2 = 50,000

N = 130x2 =26

Semiannual YTM = 11%/2 = 5.5%

We need to use PV of$1 factor and PVAF for discounting the coupon payments and Face value of the bond

PVF (5.5%,26) = 0.2486

PVAF (5.5%, 26) = 13.6624

Price = PVAF x PMT + FV x PVF

1,000,000 = (13.6624x 50,000) + ( FV x 0.2486)

1000,000= 683120+ ( FV x 0.2486)

subtracting 683120 from both sides we get:

316880 = FV x 0.2486

dividing both sides by 0.2486, we get:

FV =$1,274,658

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