Chapter 16, Problem 58P

Pensacola Cablevision Company provides television cable service to two counties in the Florida panhandle. The firm’s management is considering the construction of a new satellite dish in December of 20x0. The new antenna would improve reception and the service provided to customers. The dish antenna and associated equipment will cost $200,000 to purchase and install. The company’s old equipment, which is fully depreciated, can be sold now for $20,000. The company president expects the firm’s improved capabilities to result in additional revenue of $80,000 per year during the dish’s useful life of seven years. The incremental operating expenses associated with the new equipment are projected to be $10,000 per year. These incremental revenues and expenses are in real dollars.

The new satellite dish will be depreciated under the MACRS depreciation schedule for the 5-year property class. The company’s tax rate is 40 percent.

Pensacola Cablevision’s president expects the real rate of interest in the economy to remain stable at 10 percent. She expects the inflation rate, currently running at 20 percent, to remain unchanged.

Required:

1. 1. Compute the price index for each year from 20x1 through 20x7, using 1.0000 as the index for 20x0.
2. 2. Prepare a schedule of after-tax cash flows measured in real dollars.
3. 3. Compute the net present value of the proposed new satellite dish using cash flows measured in real dollars. Use a real discount rate equal to the real interest rate.

To determine

Calculate the price index of new satellite dish for each year.

Explanation of Solution

Cash inflows: The amount of cash received by a company from the operating, investing, and financing activities of the business during a certain period is referred to as cash inflow.

Cash outflows: The amount of cash paid by a company for the operating, investing, and financing activities of the business during a certain period is referred to as cash outflow.

Calculate the price index of new satellite dish for each year as follows:

Year	Price factor	Price factor for each year	Price index
20x1	1.20	(1.20)1	1.2000
20x2	1.20	(1.20)2	1.4400
20x3	1.20	(1.20)3	1.7280
20x4	1.20	(1.20)4	2.0736
20x5	1.20	(1.20)5	2.4883
20x6	1.20	(1.20)6	2.9860
20x7	1.20	(1.20)7	3.5832

Table (1)

Note: Normal price rate of 100% is taken as 1 and the inflation rate of 20% is taken as 0.20. Hence, the price factor is 1.20$\left(1.00+0.20\right)$.

To determine

Prepare a schedule of after tax cash flow measured in real dollars.

Explanation of Solution

Prepare a schedule of after tax cash flow measured in real dollars as follows:

Cash outflow:

$\begin{array}{c}\text{Net cash outflow = }\left(\left(\text{Acquisation cost+Gain}\right)-\text{Salvage value}\right)\\ =\left(\$200,000+\$8,000(3)\right)-\$20,000\\ =\$188,000\end{array}$

Cash inflows:

Schedule for the cash inflows
Year	After tax operating cost savings (2) (F)	Depreciation expense (1) (G)	After tax cash flow in real dollars$\left(F+G\right)$
20x1	$42,000	$13,333	$55,333
20x2	$42,000	$17,778	$59,778
20x3	$42,000	$8,889	$50,889
20x4	$42,000	$4,444	$46,444
20x5	$42,000	$3,704	$45,704
20x6	$42,000	$1,543	$43,543
20x7	$42,000	-	$42,000

Table (2)

Working note (1):

Calculate the depreciation expense under MACRS.

Depreciation Schedule
Year	MACRS Percentage (A)	Depreciation $B=\left(A\times \$200,000\right)$	Tax Rate (C)	Depreciation expense $D=\left(B\times C\right)$	Price index (E)	Depreciation tax shield in real dollars $\left(D\times E\right)$
20x1	20.00%	$ 40,000	40%	$16,000	1.2000	$13,333
20x2	32.00%	$64,000	40%	$25,600	1.4400	$17,778
20x3	19.20%	$38,400	40%	$15,360	1.7280	$8,889
20x4	11.52%	$23,040	40%	$9,216	2.0736	$4,444
20x5	11.52%	$23,040	40%	$9,216	2.4883	$3,704
20x6	5.67%	$11,520	40%	$4,608	2.9860	$1,543
20x7	-	-		-	3.5832	-

Table (3)

Working note (2):

Calculate the after tax incremental cash inflow.

$\begin{array}{c}\begin{array}{l}\text{After tax incremental }\\ \text{cash inflow }\end{array}\}\text{= }\left(\begin{array}{l}\text{Operating revenue}-\\ \text{Operating expense}\end{array}\right)\times \left(\text{1}-\text{Tax}\text{rate}\right)\\ =\left(\$80,000-\$10,000\right)\times \left(1-\frac{40}{100}\right)\\ =\$42,000\end{array}$

Working note (3):

Calculate the after tax gain on sale of old equipment.

$\begin{array}{c}\text{After tax gain on old equipment = Replacement cost of old equipment}\times \text{Tax rate}\\ \text{=\$20,000}\times \left(\frac{40}{100}\right)\\ =\$8,000\end{array}$

To determine

Calculate the net present value of new satellite dish.

Explanation of Solution

Year	Cash inflow (H)	Present value factor @10% (I)	Present value $\left(H\times I\right)$
20x1	$55,333	0.909	$50,298
20x2	$59,778	0.826	$49,377
20x3	$50,889	0.751	$38,218
20x4	$46,444	0.683	$31,721
20x5	$45,704	0.621	$28,382
20x6	$43,543	0.564	$24,558
20x7	$42,000	0.513	$21,546
Total present value			$ 244,100
Less: Cash outflow for investment			$ 188,000
Net present value			$ 56,100

Table (4)

Note: Refer Appendix A (table III) for the present value factor.

Conclusion

Therefore, the net present value of new satellite dish is $56,100.