Question

a) A company expects a series of 24 monthly receipts of $3,600 each. The first payment will be received 1 month from today. Determine the present value of this series assuming an interest rate of 12% per year compounded semiannually.

b）ANB ltd has common equity of $35.5mn and $31.9mn of long-term debt and $10.3mn of preferred equity on its books. Required return on these funds are 12%, 8%, and 10%, respectively. Market values of the common equity and long-term debt are $46.6mn and $35mn, respectively. Market value of preferred equity is the same as its book value. Estimate WACC for the company given that its effective tax rate is 30%.

Answer 1

a)	Number of payments to be received = 24 months
	Monthly Receipts = $ 3600 each
	Interest rate = 12% per year compounded semiannually
	We need 12% per year compounded per year
	Therefore, the effective annual rate would be
	Semi Annual Rate = 12/2 = 6%
	(1.06)^2 - 1		12.36%
	Monthly Interest Rate = 12.36%/12			1.03%
	We need to calculate present value of $ 3600 received for 24 months as today by discounting the receipts
	Months	Cash inflow	Discount Factor @ 12.36%(1/(1.1236^n)		Present Value
	1	$3,600	0.9898	1/(1.0103^1)	$3,563.30
	2	$3,600	0.9797	1/(1.0103^2)	$3,526.97
	3	$3,600	0.9697	1/(1.0103^3)	$3,491.01
	4	$3,600	0.9598	1/(1.0103^4)	$3,455.42
	5	$3,600	0.9501	1/(1.0103^5)	$3,420.19
	6	$3,600	0.9404	1/(1.0103^6)	$3,385.33
	7	$3,600	0.9308	1/(1.0103^7)	$3,350.81
	8	$3,600	0.9213	1/(1.0103^8)	$3,316.65
	9	$3,600	0.9119	1/(1.0103^9)	$3,282.84
	10	$3,600	0.9026	1/(1.0103^10)	$3,249.37
	11	$3,600	0.8934	1/(1.0103^11)	$3,216.24
	12	$3,600	0.8843	1/(1.0103^12)	$3,183.45
	13	$3,600	0.8753	1/(1.0103^13)	$3,151.00
	14	$3,600	0.8664	1/(1.0103^14)	$3,118.87
	15	$3,600	0.8575	1/(1.0103^15)	$3,087.08
	16	$3,600	0.8488	1/(1.0103^16)	$3,055.60
	17	$3,600	0.8401	1/(1.0103^17)	$3,024.45
	18	$3,600	0.8316	1/(1.0103^18)	$2,993.62
	19	$3,600	0.8231	1/(1.0103^19)	$2,963.10
	20	$3,600	0.8147	1/(1.0103^20)	$2,932.89
	21	$3,600	0.8064	1/(1.0103^21)	$2,902.99
	22	$3,600	0.7982	1/(1.0103^22)	$2,873.39
	23	$3,600	0.7900	1/(1.0103^23)	$2,844.10
	24	$3,600	0.7820	1/(1.0103^24)	$2,815.10
		Present Value of series			$76,203.76
		Present Value of monthly Payment is $ 76203.76
		Alternatively can be calculated using the PV function
		$76,203.76		PV(1.03%,24,-3600)
b)	The WACC of the firm can be calculated either based on the book value weights of capital or market value weights of capital, since nothing is mentioned we would estimate WACC by using both the methods
	Cost of Equity = 12%
	After Tax cost of debt = 8%*(1-0.30)			5.60%
	Cost of Preferred stock = 10%
	Weights based on Book Value
		Book Value (In mn)	Weights
	Common Equity	$35.50	0.4569	35.50/77.70
	Long Term Debt	$31.90	0.4106	31.90/77.70
	Preferred Equity	$10.30	0.1326	10.30/77.70
		$77.70
	WACC = 0.12*0.4569 + 0.056*0.4106 + 0.10*0.1326
		9.11%
	Weights based on Market Value
		Book Value (In mn)	Weights
	Common Equity	$46.60	0.5071	46.60/91.90
	Long Term Debt	$35.00	0.3808	35/91.90
	Preferred Equity	$10.30	0.1121	10.30/91.90
		$91.90
	WACC = 0.12*0.5071 + 0.056*0.3808 + 0.10*0.1121
		9.34%