Question

Hard Spun Industries (HSI) has a project that it expects will produce a cash flow of $2.9 million in 10 years. To finance the project, the company needs to borrow $1.7 million today. The project will also produce intermediate cash flows of $170,000 per year that HSI can use to service coupon payments of $85,000 every six months. Based on the risk of this investment, market participants will require a 11.0% yield. If HSI wishes a maturity of 10 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. (Enter just the number in dollars without the $ sign or a comma and round off decimals to the closest integer, i.e., rounding $30.49 down to $30 and rounding $30.50 up to $31.)

Answer 1

Formula sheet

A	B	C	D	E	F	G	H
2
3		Current Price of Bond should be equal to the amount to be borrowed today.
4
5		Current Price of Bond	=Amount to be borrowed
6			1700000
7
8		Assuming the Face value is F, then
9		Face Value	F
10		Maturity of bond	10	Year
11		Market Interest rate	0.11
12		Semi-Annual Coupon of Bond	85000
13		Semi-Annual Period (C)	=D10*2
14		Semi-annual Interest Rate (i)	=D11/2	=D11/2
15
16		Since current Price of bond is the present value of future cash flows, therefore
17		Current Price of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
18			=$85,000*(P/A,5.50%,20)+F*(P/F,5.50%,20)
19
20		Using the following Factor,
21		(P/A,5.50%,20)	=PV(D14,D13,-1,0)	=PV(D14,D13,-1,0)
22		(P/F,5.50%,20)	=1/((1+D14)^D13)	=1/((1+D14)^D13)
23
24		Current Price of Bond	=$85,000*(P/A,5.50%,20)+F*(P/F,5.50%,20)
25			=$85,000*11.95+F*0.34
26
27		Since current price of bond is	=D6
28		therefore,
29		1,700,000=$85,000*11.95+F*0.34
30
31		Solving the above equation,
32
33		F=	=(D27-(D12*D21))/D22	=(D27-(D12*D21))/D22
34
35		Hence Face value of bond should be	=D33
36