Math / Data & Statistics

QuestionQuestion 2 Robinson Co. is interested in purchasing a new delivery vehicle so it can become a subcontractor with Amazon Logistics. The vehicle would cost $\$ 75,000$ and generate delivery revenue of $\$ 30,000$ for each of the next 6 years. If Robinson Co. purchases the vehicle, it will take a loan for $\$ 60,000$ . The terms of the loan stipulate that $4 \%$ annual interest would be charged and that the loan would be repaid in 6 equal end of year payments. At the end of the 6 years, the vehicle will have a salvage value of $\$ 10,000$ . The tax rate is $40 \%$ . Assuming that the vehicle is depreciated using MACRS (5-year property class) and that Robinson Co. uses an after-tax MARR of 10\%, compute the PW and determine whether Robinson Co. should purchase the new business vehicle. ( 25 points)

Studdy Solution

STEP 1

What is this asking? Should Robinson Co. buy a delivery vehicle for their business, considering its cost, the loan, the revenue it generates, its depreciation, and the eventual salvage value? Watch out! Don't forget to factor in taxes and the time value of money using the MARR!

STEP 2

1. Calculate yearly loan payment
2. Calculate depreciation
3. Calculate net cash flow
4. Calculate present worth

STEP 3

We're dealing with a loan, so let's figure out the yearly payment!
We'll use the present value of an annuity formula.
The present value $PV$ is the loan amount, which is $\$60{,}000$ .
The interest rate $i$ is $4\%$ , or $0.04$ .
The number of periods $n$ is $6$ years.
The formula is:
$PV = PMT \cdot \frac{1 - (1 + i)^{-n}}{i}$

STEP 4

Let's plug in our values and solve for the yearly payment ( $PMT$ ):
$\$60{,}000 = PMT \cdot \frac{1 - (1 + 0.04)^{-6}}{0.04}$ $PMT = \frac{\$60{,}000}{\frac{1 - (1.04)^{-6}}{0.04}}$ $PMT = \frac{\$60{,}000}{5.2421}$ $PMT \approx \$11{,}445.67$ So, the yearly loan payment is approximately $\$11{,}445.67$ .

STEP 5

The vehicle is a 5-year property, so we'll use the MACRS 5-year depreciation schedule.
The percentages are: 20%, 32%, 19.2%, 11.52%, 11.52%, and 5.76%.
We multiply these percentages by the vehicle's initial cost of $\$75{,}000$ to get the depreciation for each year.

STEP 6

Here's the depreciation for each year:
* Year 1: $0.20 \cdot \$75{,}000 = \$15{,}000$ * Year 2: $0.32 \cdot \$75{,}000 = \$24{,}000$ * Year 3: $0.192 \cdot \$75{,}000 = \$14{,}400$ * Year 4: $0.1152 \cdot \$75{,}000 = \$8{,}640$ * Year 5: $0.1152 \cdot \$75{,}000 = \$8{,}640$ * Year 6: $0.0576 \cdot \$75{,}000 = \$4{,}320$

STEP 7

For each year, the net cash flow is the revenue minus the loan payment, plus the tax savings from depreciation.
The tax savings is the depreciation amount multiplied by the tax rate of $40\%$ .
The revenue is a constant $\$30{,}000$ each year.

STEP 8

Let's calculate the net cash flow for each year:
* Year 1: $\$30{,}000 - \$11{,}445.67 + (\$15{,}000 \cdot 0.40) = \$24{,}554.33$ * Year 2: $\$30{,}000 - \$11{,}445.67 + (\$24{,}000 \cdot 0.40) = \$28{,}154.33$ * Year 3: $\$30{,}000 - \$11{,}445.67 + (\$14{,}400 \cdot 0.40) = \$24{,}314.33$ * Year 4: $\$30{,}000 - \$11{,}445.67 + (\$8{,}640 \cdot 0.40) = \$21{,}994.33$ * Year 5: $\$30{,}000 - \$11{,}445.67 + (\$8{,}640 \cdot 0.40) = \$21{,}994.33$ * Year 6: $\$30{,}000 - \$11{,}445.67 + (\$4{,}320 \cdot 0.40) + \$10{,}000 = \$29{,}282.33$ (Salvage value added in year 6!)

STEP 9

Now, we'll calculate the present worth of these cash flows using the MARR of $10\%$ .
The formula for present worth is:
$PW = \sum_{t=1}^{n} \frac{CF_t}{(1 + MARR)^t}$ where $CF_t$ is the cash flow in year $t$ .

STEP 10

Let's plug in the values:
$PW = \frac{\$24{,}554.33}{1.10} + \frac{\$28{,}154.33}{1.10^2} + \frac{\$24{,}314.33}{1.10^3} + \frac{\$21{,}994.33}{1.10^4} + \frac{\$21{,}994.33}{1.10^5} + \frac{\$29{,}282.33}{1.10^6}$ $PW \approx \$22{,}322.12 + \$23{,}268.04 + \$18{,}057.91 + \$14{,}876.74 + \$13{,}524.31 + \$16{,}526.33$ $PW \approx \$108{,}575.45$

STEP 11

The present worth of the investment is approximately $\$108{,}575.45$ .
Since the PW is positive, Robinson Co. should purchase the vehicle!

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Studdy Solution

STEP 1

What is this asking? Should Robinson Co. buy a delivery vehicle for their business, considering its cost, the loan, the revenue it generates, its depreciation, and the eventual salvage value? Watch out! Don't forget to factor in taxes and the time value of money using the MARR!

STEP 2

1. Calculate yearly loan payment
2. Calculate depreciation
3. Calculate net cash flow
4. Calculate present worth

STEP 3

STEP 4

STEP 5

The vehicle is a 5-year property, so we'll use the MACRS 5-year depreciation schedule.
The percentages are: 20%, 32%, 19.2%, 11.52%, 11.52%, and 5.76%.
We multiply these percentages by the vehicle's initial cost of $\$75{,}000$ to get the depreciation for each year.

STEP 6

STEP 7

For each year, the net cash flow is the revenue minus the loan payment, plus the tax savings from depreciation.
The tax savings is the depreciation amount multiplied by the tax rate of $40\%$ .
The revenue is a constant $\$30{,}000$ each year.

STEP 8

STEP 9

Now, we'll calculate the present worth of these cash flows using the MARR of $10\%$ .
The formula for present worth is:
$PW = \sum_{t=1}^{n} \frac{CF_t}{(1 + MARR)^t}$ where $CF_t$ is the cash flow in year $t$ .

STEP 10

STEP 11

The present worth of the investment is approximately $\$108{,}575.45$ .
Since the PW is positive, Robinson Co. should purchase the vehicle!

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Studdy Solution

STEP 1

What is this asking? Should Robinson Co. buy a delivery vehicle for their business, considering its cost, the loan, the revenue it generates, its depreciation, and the eventual salvage value? Watch out! Don't forget to factor in taxes and the time value of money using the MARR!

STEP 2

1. Calculate yearly loan payment2. Calculate depreciation3. Calculate net cash flow4. Calculate present worth

STEP 3

STEP 4

STEP 5

The vehicle is a 5-year property, so we'll use the **MACRS 5-year depreciation schedule**.The percentages are: 20%, 32%, 19.2%, 11.52%, 11.52%, and 5.76%.We **multiply** these percentages by the vehicle's **initial cost** of $75,000\$75{,}000$75,000 to get the depreciation for each year.

STEP 6

STEP 7

For each year, the **net cash flow** is the **revenue** minus the **loan payment**, plus the **tax savings from depreciation**.The tax savings is the depreciation amount multiplied by the **tax rate** of 40%40\%40%.The revenue is a constant $30,000\$30{,}000$30,000 each year.

STEP 8

STEP 9

Now, we'll **calculate the present worth** of these cash flows using the **MARR** of 10%10\%10%.The formula for present worth is:PW=∑t=1nCFt(1+MARR)t PW = \sum_{t=1}^{n} \frac{CF_t}{(1 + MARR)^t} PW=t=1∑n​(1+MARR)tCFt​​where CFtCF_tCFt​ is the cash flow in year ttt.

STEP 10

STEP 11

The present worth of the investment is approximately $108,575.45\$108{,}575.45$108,575.45.Since the PW is **positive**, Robinson Co. *should* purchase the vehicle!

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1. Calculate yearly loan payment
2. Calculate depreciation
3. Calculate net cash flow
4. Calculate present worth

The vehicle is a 5-year property, so we'll use the MACRS 5-year depreciation schedule.
The percentages are: 20%, 32%, 19.2%, 11.52%, 11.52%, and 5.76%.
We multiply these percentages by the vehicle's initial cost of $\$75{,}000$ to get the depreciation for each year.

For each year, the net cash flow is the revenue minus the loan payment, plus the tax savings from depreciation.
The tax savings is the depreciation amount multiplied by the tax rate of $40\%$ .
The revenue is a constant $\$30{,}000$ each year.

Now, we'll calculate the present worth of these cash flows using the MARR of $10\%$ .
The formula for present worth is:
$PW = \sum_{t=1}^{n} \frac{CF_t}{(1 + MARR)^t}$ where $CF_t$ is the cash flow in year $t$ .

The present worth of the investment is approximately $\$108{,}575.45$ .
Since the PW is positive, Robinson Co. should purchase the vehicle!