Question

Station WJXT is considering the replacement of its old fully depreciated sound mixer. Two new models are available. Mixer X has a cost of $345,000, a 15-year life, and after-tax cash flows (including the tax shield from depreciation) of $70,000 per year. Mixer Y has a cost of $130,000, a 5-year expected life, and after-tax cash flows (including the tax shield from depreciation) of $60,000 per year. No new technological developments are expected. The discount rate is 12 percent. Should WJXT replace the old mixer, and, if so, with X or Y? (Hint: If WJXT chooses mixer Y, it can always buy a one when the old one is out of use after its economic life. Since there are no technological developments, the new mixer Y will generate the same cashflow)

Answer 1

Station WJXT should replacement the old fully depreciated sound mixer since the old mixer has completed the economic useful life.

The total discounted Cash Outflow if WJXT buy Mixer X = $ 345,000

The total discounted Cash inflow if WJXT buy Mixer X = $ 476,760

The Net Cash Inflow for Mixer X $ 131760

The total discounted Cash Outflow if WJXT buy Mixer Y = $ 245,622

The total discounted Cash inflow if WJXT buy Mixer Y= $ 408,651

The Net Cash Inflow for Mixer Y $ 163,029

Mixer Y can be selected since the Net Cash Inflow for Mixer Y is $ 31,269

Please find below the working for the calculation.

	Mixer X					Mixer Y
Year			Life 15 Years			Mixer Y		Life 5 Years			Discounted rate @ 12%
	Cash Outflow	Discounted Cash Outflow	Cash Inflow	Discounted Cash Inflow	Discounted CashFlow	Cash Outflow	Discounted Cash Outflow	Cash Inflow	Discounted Cash Inflow	Discounted CashFlow		Net Cash Difference
	(1)		(2)		(3)	(4)		(5)		(6)	(7)	(8)
	(1)		(2)		((2)-(1))X(8) ='(3)	(4)		(5)		((5)-(4))X(8) =(6)	(7)	(3)-(6) =(8)
0	345,000.00	345,000.00		-	-345,000.00	130,000.00	130,000.00		-	-130,000.00	1.00	-215,000.00
1		-	70,000.00	62,500.00	62,500.00		-	60,000.00	53,571.43	53,571.43	0.89	8,928.57
2		-	70,000.00	55,803.57	55,803.57		-	60,000.00	47,831.63	47,831.63	0.80	7,971.94
3		-	70,000.00	49,824.62	49,824.62		-	60,000.00	42,706.81	42,706.81	0.71	7,117.80
4		-	70,000.00	44,486.27	44,486.27		-	60,000.00	38,131.08	38,131.08	0.64	6,355.18
5		-	70,000.00	39,719.88	39,719.88	130,000.00	73,765.49	60,000.00	34,045.61	-39,719.88	0.57	79,439.76
6		-	70,000.00	35,464.18	35,464.18		-	60,000.00	30,397.87	30,397.87	0.51	5,066.31
7		-	70,000.00	31,664.45	31,664.45		-	60,000.00	27,140.95	27,140.95	0.45	4,523.49
8		-	70,000.00	28,271.83	28,271.83		-	60,000.00	24,232.99	24,232.99	0.40	4,038.83
9		-	70,000.00	25,242.70	25,242.70		-	60,000.00	21,636.60	21,636.60	0.36	3,606.10
10		-	70,000.00	22,538.13	22,538.13	130,000.00	41,856.52	60,000.00	19,318.39	-22,538.13	0.32	45,076.25
11		-	70,000.00	20,123.33	20,123.33		-	60,000.00	17,248.57	17,248.57	0.29	2,874.76
12		-	70,000.00	17,967.26	17,967.26		-	60,000.00	15,400.51	15,400.51	0.26	2,566.75
13		-	70,000.00	16,042.19	16,042.19		-	60,000.00	13,750.45	13,750.45	0.23	2,291.74
14		-	70,000.00	14,323.39	14,323.39		-	60,000.00	12,277.19	12,277.19	0.20	2,046.20
15		-	70,000.00	12,788.74	12,788.74		-	60,000.00	10,961.78	10,961.78	0.18	1,826.96
Total	345,000.00	345,000.00	1,050,000.00	476,760.51	131,760.51	390,000.00	245,622.01	900,000.00	408,651.87	163,029.86		-31,269.34