Thank you for visiting Ten years ago Jacobson Recovery purchased a wrecker for 285 000 to move disabled 18 wheelers He anticipated a salvage value of 50 000 ten. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Answer:
NPV = $24,910.26
The investment is economically justified because it increases the wealth pg Jacobson Recovery by $24,910.26
Explanation:
To determine whether the investment is justifiable we will compute the the Net present Value of the project
The Net present value (NPV) is the difference between the Present value (PV) of cash inflows and the PV of cash outflows. A positive NPV implies a good and profitable investment project and a negative figure implies the opposite.
NPV = PV of cash inflows - PV of cash outflows
PV of cash average revenue = A × (1-(1+r)^(-n))/r
A- average revenue, r- discount ate- 12% , n- number of years- 10
PV of reveue = 52,000 × (1-(1.12)^(-10)/0.12= $293,811.60
PV of salvage value = F × (1+r)^(-n)
= 50,000 × 1.12^(-10)
= 16,098.66183
NPV = $293,811.60 + 16,098.66183 - $285,000
= $24,910.26
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Rewritten by : Jeany
The final answer is: [tex]\[ NPV = \$88,874 \][/tex]
To determine if Jacobson Recovery's investment in the wrecker was economically justified at a 12% discount rate, we need to calculate the Net Present Value (NPV) of the investment. The NPV is the sum of the present values of all cash flows (both incoming and outgoing) over the life of the investment.
The initial investment (outgoing cash flow) is $285,000. The salvage value (incoming cash flow at the end of 10 years) is $50,000. The annual revenue (incoming cash flow) is $52,000 for 10 years.
The formula for NPV is:
[tex]\[ NPV = -C_0 + \sum_{t=1}^{n} \frac{C_t}{(1+r)^t} \][/tex]
where:
- [tex]\( C_0 \)[/tex] is the initial investment
- [tex]\( C_t \)[/tex] is the net cash inflow during the period t
- [tex]\( r \)[/tex] is the discount rate
- [tex]\( n \)[/tex] is the number of periods
Let's calculate the NPV:
1. Present value of the initial investment (at [tex]\( t = 0 \)[/tex]):
[tex]\[ -C_0 = -\$285,000 \][/tex]
2. Present value of the salvage value (at [tex]\( t = 10 \)[/tex]):
[tex]\[ \frac{\$50,000}{(1+0.12)^{10}} \approx \$50,000 \times 0.211 \approx \$10,550 \][/tex]
3. Present value of the annual revenue (for [tex]\( t = 1 \) to \( t = 10 \)[/tex]):
[tex]\[ \sum_{t=1}^{10} \frac{\$52,000}{(1+0.12)^t} \][/tex]
To simplify the calculation, we can use the formula for the sum of a geometric series:
[tex]\[ \sum_{t=1}^{n} a \times r^{t-1} = a \times \frac{1-r^n}{1-r} \][/tex]
where [tex]\( a \)[/tex] is the first term of the series and [tex]\( r \)[/tex] is the common ratio. In this case, [tex]\( a = \$52,000 \)[/tex] and [tex]\( r = \frac{1}{1+0.12} \)[/tex].
[tex]\[ \sum_{t=1}^{10} \frac{\$52,000}{(1+0.12)^t} = \$52,000 \times \frac{1-\left(\frac{1}{1+0.12}\right)^{10}}{1-\frac{1}{1+0.12}} \][/tex]
[tex]\[ \approx \$52,000 \times \frac{1-0.211}{1-0.893} \][/tex]
[tex]\[ \approx \$52,000 \times \frac{0.789}{0.107} \][/tex]
[tex]\[ \approx \$52,000 \times 7.377 \][/tex]
[tex]\[ \approx \$383,324 \][/tex]
Now, we can calculate the NPV:
[tex]\[ NPV = -\$285,000 + \$10,550 + \$383,324 \][/tex]
[tex]\[ NPV = -\$285,000 + \$393,874 \][/tex]
[tex]\[ NPV = \$88,874 \][/tex]
Since the NPV is positive, the investment is economically justified at a 12% discount rate. Jacobson Recovery's decision to purchase the wrecker would be considered a good investment under these conditions.
