Question 18.6: Your S corporation needs a new truck for its operations and ...
Your S corporation needs a new truck for its operations and is looking at three alternatives. The first alternative is to lease the truck for sixty months. The monthly lease payment is $525 per month with the first payment due in April. At the end of the lease the truck will be returned to the dealer. The lease is considered an operating lease and excludes all maintenance and operational costs. The second alternative is to purchase the truck with a sixty-month loan at an interest rate of 9% (APY 9.38). The loan has $250 in origination fees. The truck’s entire sales price of $25,000— including the loan origination fees—can be financed. The first payment is due in April. The third alternative is to purchase the truck with cash for $25,000 in April. If your company purchases the truck, the estimated salvage value of the truck at the end of five years is $5,000. Gains and losses on the sale of the truck will be treated as ordinary income. The truck may be depreciated using the half-year convention. For all three alternatives, the truck is to be placed in service in April. Your company’s tax year is the same as the calendar year and its marginal tax rate is 34%. Using the net present value (cost) method, which of the above alternatives is the best for your company if your minimal acceptable rate of return (MARR) is 1% per month? Assume that there is sufficient taxable income to use all tax savings in the year they occur.
The costs for each month can be easily determined; therefore, we use a period length of one month. Because the company is an S corporation that will pay income taxes at the individual level, periodic tax payments are due in April, June, September, and January of the following year. The useful life of the truck will be from April of the first year to March of the sixth year. The income tax savings or costs for the sixth year will occur in April, June, and September of the sixth year and January of the seventh year; therefore, the study period will be from April of the first year to January of the seventh year. Solving this problem is best done using a spreadsheet because each option will require seventy periods to cover the study period. The spreadsheet solutions are shown in Figures 18-1, 18-4, and 18-5.
First, we calculate the net present value for the first alternative, leasing the truck. The after-tax cost for each month is the lease payment less the tax savings, which occur only in the months of April, June, September, and January. The tax savings for the first year are divided equally among the four months and are calculated as follows:
Tax Savings_1 = $525.00/month(9 months)(0.34)/4 = $401.63
The after-tax cost for the first month—April—is calculated as follows:
After-Tax Cost_{1} = -$525.00 + $401.63 = -$123.37
The present value of the after-tax cost for the first month is calculated using Eq. (15-3) as follows:
P = F/(1 + i)^n (15-3)
P_1 = -$123.37/(1 + 0.01)^1 = -$122.15
Because no tax savings occur in the second month May—the after-tax cost equals the costs of the lease. The present value of the after-tax cost for the second month is calculated using Eq. (15-3) as follows:
P_2 = -$525.00/(1 + 0.01)^2 = -$514.66
The after-tax costs and present values of the third through seventienth months are calculated in a similar manner. Keep in mind that the lease cost will go to zero in the sixty-first month, the tax savings will change beginning with the thirteenth month—April of the second year and again beginning with the sixty first month—April of the sixth year. The tax savings for the thirteenth and sixty-first months are calculated as follows:
Tax Savings_{13} = $525.00/month(12 months)(0.34)/4 = $535.50
Tax Savings_{61} = $525.00/month(3 months)(0.34)/4 = $133.88
The spreadsheet solution for the lease option is shown in Figure 18-1. The differences between the spreadsheet solution and this example are because of rounding errors in the example.
Summing the present values, we get a net present cost of $15,686.
Next, we calculate the net present value for the second alternative, purchasing the truck with a sixty-month loan. The after-tax cost for each month is the loan payment less the tax savings. As in the lease option, the tax savings are spread equally among the months of April, June, September, and January. The tax savings result from the interest paid on the loan and the depreciation of the truck. To calculate the tax savings, the interest paid on the loan each year needs to be calculated. This may be done in two ways. The first way is to use Eq. (16-7) to determine the monthly payment, Eq. (16-13) to determine the outstanding balance at the end of each year, and Eq. (16-14) to determine the annual interest costs. The periodic rate is calculated using Eq. (16-3) as follows:
A = P[i(1 + i)^n]/[1 + i)^n – 1] (16-7)
where
P = Principal
i = Periodic Interest Rate for One Month
n = Duration of Loan in Months
U_t = A[(1 + i)^{(n-t)} – 1]/[i(1 + i)^{(n-t)} ] (16-13)
where
U_t = Outstanding Principal Balance of the End of Month t
A = Monthly Payment
i = Monthly Interest Rate
n = Duration of Loan in Months
t = Number of Monthly Payments That Have Been Made
I = N(A) + U_t – U_{t-N} (16-14)
where
I = Interest Due for a Period of N Months
N = Number of Monthly Payments Made Between Two Periods
A = Monthly Payment
U_t = Outstanding Principal at the End of the Last Period Outstanding Principal at the Beginning of the First Period (t – N)
i = r/c (16-3)
where
i = Periodic Interest Rate
r = Nominal Interest Rate per Year or Annual Percentage Rate (APR)
c = Number of Compounding Periods in a Year where c ≥ 1
i = 0.09/12 = 0.0075
The initial loan value equals $25,250—the cost of the truck plus the loan origination fees. Using Eq. (16-7) to calculate the monthly loan payments we get the following:
A = $25,250[0.0075(1 + 0.0075)^{60}] /[(1 + 0.0075)^{60} – 1] = $524.15
The outstanding balance on the loan for years 1 through 6 is calculated using Eq. (16-13) as follows:
U_9 = $524.15[(1 + 0.0075)^{60-9} – 1] / [0.0075(1 + 0.0075)^{60-9}]
U_9 = $22,145.11
U_{21} = $524.15[(1 + 0.0075)^{60-21} -1] /[0.0075(1 + 0.0075)^{60-21}]
U_{21} = $17,666.63
U_{33} = $524.15[(1 – 0.0075)^{60-33} – 1] / [0.0075(1 + 0.0075)^{60-33}]
U_{33} = $12,768.03
U_{45} = $524.15[(1 + 0.0075)^{60-45} – 1] / [0.0075(1 + 0.0075)^{60-45}]
U_{45} = $7,409.91
U_{57} = $524.15[(1 + 0.0075)^{60-57} – 1] / [0.0075(1 + 0.0075)^{60-57}]
U_{57} = $1,549.15
U_{60} = $524.15[(1 + 0.0075)^{60-60} – 1] / [0.0075(1 + 0.0075)^{60-60}]
= $0
The annual interest paid each year is calculated using Eq. (16-14) as follows:
I_{1-9} = 9($524.15) + $22,145.11 – $25,250.00 = $1,612.46
I_{10-21} = 12($524.15) + $17,666.63 – $22,145.11 = $1,811.32
I_{22-33} = 12($524.15) + $12,768.03 – $17,666.63 = $1,391.20
I_{34-45} = 12($524.15) + $7,409.91 – $12,768.03 = $931.68
I_{46-57} = 12($524.15) + $1,549.15 – $7,409.91 = $429.04
I_{58-60} = 3($524.15) + $0 – $1,549.15 = $23.30
The second way is to prepare a loan amortization schedule. Because the payments are made monthly, the amortization schedule will cover sixty months beginning with April of year 1 and ending in March of year 6. The amortization schedule for the loan is shown in Figures 18-2 and 18-3 and was prepared as shown in Chapter 16. Included on the amortization schedule is a column showing the year-to-date totals for both the monthly payments and the interest paid. Note that the last payment is slightly smaller due to rounding of the monthly payment and monthly interest.
For income tax purposes, the loan payment is not deductible; however, the interest on the loan is deductible. The interest itself is not a cash flow because it has already been included in the cash flow for the loan payment.
In addition to interest, depreciation is also tax deductible. Like interest, depreciation is not a cash flow but is necessary to calculate the cash flow due to tax savings. From Table 5-6 the depreciation for the truck is calculated as follows:
| TABLE 5-6^{18} Depreciation Rates for 200% Declining Balance Using the Half-Year Convention | ||||
| YEAR | 3 YEARS (%) | 5 YEARS (%) | 7 YEARS (%) | 10 YEARS (%) |
| 1 | 33.33 | 20.00 | 14.29 | 10.00 |
| 2 | 44.45 | 32.00 | 24.49 | 18.00 |
| 3 | 14.81 | 19.20 | 17.49 | 14.40 |
| 4 | 7.41 | 11.52 | 12.49 | 11.52 |
| 5 | NA | 11.52 | 8.93 | 9.22 |
| 6 | NA | 5.76 | 8.92 | 7.37 |
| 7 | NA | NA | 8.93 | 6.55 |
| 8 | NA | NA | 4.46 | 6.55 |
| 9 | NA | NA | NA | 6.56 |
| 10 | NA | NA | NA | 6.55 |
| 11 | NA | NA | NA | 3.28 |
D_{1-9} = ($25,000)0.2000 = $5,000
D_{10-21} = ($25,000)0.3200 = $8,000
D_{22-33} = ($25,000)0.1920 = $4,800
D_{34-45} = ($25,000)0.1152 = $2,880
D_{46-57} = ($25,000)0.1152 = $2,880
D_{58-60} = ($25,000)0.0576 = $1,440
The disposal of the truck will result in a gain or loss, which will be treated as ordinary income or ordinary loss. The book value will be equal to the purchase price less the depreciation taken and is calculated as follows:
BV_{60} = $25,000 – $5,000 – $8,000 – $4,800 – $2,880 – $2,880
-$1,440
BV_{60} = $0
Because the truck is sold for more that its book value, a gain will occur in the sixth year. The gain is equal to the difference in the salvage value and the book value and is calculated as follows.
Capital Gain = $5,000 – $0 = $5,000
The tax savings are equal to the sum of the interest paid and the depreciation multiplied by the marginal tax rate. The tax savings are similar to a cash receipt and as such are positive. The tax savings will change at the beginning of the first, thirteenth, twenty-fifth, thirty-seventh, forty-ninth, and sixty-first months and is calculated as follows:
Tax Savings_1 = ($1,612.46 + $5,000.00)(0.34)/4 = $562.05
Tax Savings_{13} = ($1,811.32 + $8,000.00)(0.34)/4 = $833.96
Tax Savings_{25} = ($1,391.20 + $4,800.00)(0.34)/4 = $526.25
Tax Savings_{37} = ($931.68 + $2,880.00)(0.34)/4 = $323.99
Tax Savings_{49} = ($429.04 + $2,880.00)(0.34)/4 = $281.27
In the sixty-first month there will be an increase in tax liability due to gains on the truck, which will be taxed at the rate of 34%. The tax savings beginning in the sixty-first month is calculated as follows:
Tax Savings_{61} = ($23.30 + $1,440.00 – $5,000.00)(0.34)/4
Tax Savings_{61} = -$300.62
The after-tax costs and present value are calculated in the same manner as they were calculated for the lease option. The spreadsheet solution for the purchase of the truck with a loan is shown in Figure 18-4. The differences between the spreadsheet solution and this example are because of rounding errors in the example.
Summing the present values, we get a net present cost of $13,378.
Next, we calculate the net present value for the third alternative, which is to purchase the truck outright for $25,000. The purchase of the truck occurs during April. For this alternative, only depreciation will be tax deductible. The depreciation will be the same for this alternative as for the second alternative. Similar the disposal of the truck in the sixth year will result in a capital gain of $5,000.
The tax savings are equal to the depreciation multiplied by the marginal tax rate and are divided among the four payments that occur during the year. The tax savings are similar to a cash receipt and as such are positive. The tax savings will change at the beginning of the first, thirteenth, twenty-fifth, thirty-seventh, forty-ninth, and sixty-first months and is calculated as follows:
Tax Savings_1 = $5,000.00(0.34)/4 = $425
Tax Savings_{13} = $8,000.00(0.34)/4 = $680
Tax Savings_{25} = $4,800.00(0.34)/4 = $408
Tax Savings_{37} = $2,880.00(0.34)/4 = $244.80
Tax Savings_{49} = $2,880.00(0.34)/4 = $244.80
In the sixty-first month there will be an increase in tax liability due to gains on the truck, which will be taxed at the rate of 34%. The tax savings beginning in the sixty-first month is calculated as follows:
Tax Savings_{61} = ($1,440.00 – $5,000.00)(0.34)/4 = -$302.60
The after-tax costs and present value are calculated in the same manner as they were calculated for the lease option. The spreadsheet solution for the purchasing the truck is shown in Figure 18-5. The differences between the spreadsheet solution and this example are because of rounding errors in the example. Summing the present values, we get a net present cost of $16,265. The purchase with a loan has the lowest net present cost; therefore, purchasing the truck with the loan is the most financially attractive alternative.
