VIPSolutionsGive step-by-step solution with explanation and final answer: Student Question Copy ID Monster Beverage is considering purchasing a new canning machine. This machine costs $ 3 , 5 0 0 , 0 0 0 up front. Required return = 1 0 . 9 % Year Cash Flow 0 $ - 3 , 5 0 0 , 0 0 0 1 $ 1 , 0 0 0 , 0 0 0 2 $ 1 , 2 0 0 , 0 0 0 3 $ 1 , 3 0 0 , 0 0 0 4 $ 9 0 0 , 0 0 0 5 $ 1 , 0 0 0 , 0 0 0 What is the present value of all future cash flows? Note: do not include value of Year 0 cash flow.
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Give step-by-step solution with explanation and final answer: Student Question Copy ID Monster Beverage is considering purchasing a new canning machine. This machine costs $ 3 , 5 0 0 , 0 0 0 up front. Required return = 1 0 . 9 % Year Cash Flow 0 $ - 3 , 5 0 0 , 0 0 0 1 $ 1 , 0 0 0 , 0 0 0 2 $ 1 , 2 0 0 , 0 0 0 3 $ 1 , 3 0 0 , 0 0 0 4 $ 9 0 0 , 0 0 0 5 $ 1 , 0 0 0 , 0 0 0 What is the present value of all future cash flows? Note: do not include value of Year 0 cash flow.
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Asked by: Kota Swarupa Rani
Created at: 2025-07-17 18:41:22
Asked by: Kota Swarupa Rani
Created at: 2025-07-17 18:41:22
Final Answer:
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Let's solve the problem **step-by-step**:
### Given Data
- **Required return (discount rate), \( r \) = 10.9% = 0.109**
- **Cash flows:**
- Year 0: \( -\$3,500,000 \) (do **not** include in PV calculation as per instructions)
- Year 1: \( \$1,000,000 \)
- Year 2: \( \$1,200,000 \)
- Year 3: \( \$1,300,000 \)
- Year 4: \( \$900,000 \)
- Year 5: \( \$1,000,000 \)
We need to find the **present value** (PV) of all future cash flows (Years 1-5), discounted at 10.9%.
---
## Step 1: Write the PV formula
Present Value of a future cash flow:
\[
PV = \frac{CF}{(1 + r)^n}
\]
Where:
- \( CF \) = Cash flow in year \( n \)
- \( r \) = Discount rate
- \( n \) = Year number
---
## Step 2: Calculate Each Year's PV
Let's do this **year by year**:
---
### **Year 1:**
\[
PV_1 = \frac{\$1,000,000}{(1 + 0.109)^1}
= \frac{\$1,000,000}{1.109}
\approx \$901,712.33
\]
---
### **Year 2:**
\[
PV_2 = \frac{\$1,200,000}{(1 + 0.109)^2}
= \frac{\$1,200,000}{1.109^2}
= \frac{\$1,200,000}{1.229881}
\approx \$975,919.77
\]
---
### **Year 3:**
\[
PV_3 = \frac{\$1,300,000}{(1 + 0.109)^3}
= \frac{\$1,300,000}{1.109^3}
= \frac{\$1,300,000}{1.364057}
\approx \$953,463.46
\]
---
### **Year 4:**
\[
PV_4 = \frac{\$900,000}{(1 + 0.109)^4}
= \frac{\$900,000}{1.109^4}
= \frac{\$900,000}{1.513753}
\approx \$594,673.50
\]
---
### **Year 5:**
\[
PV_5 = \frac{\$1,000,000}{(1 + 0.109)^5}
= \frac{\$1,000,000}{1.109^5}
= \frac{\$1,000,000}{1.680348}
\approx \$595,071.89
\]
---
## Step 3: Add All Present Values
\[
PV_{\text{total}} = PV_1 + PV_2 + PV_3 + PV_4 + PV_5
\]
\[
PV_{\text{total}} = \$901,712.33 + \$975,919.77 + \$953,463.46 + \$594,673.50 + \$595,071.89
\]
\[
PV_{\text{total}} = \$4,020,841.00
\]
---
## **Final Answer**
**The present value of all future cash flows (Years 1-5) is:**
\[
\boxed{\$4,020,841}
\]
---
**Summary Table:**
| Year | Cash Flow | PV Factor (\( (1.109)^t \)) | PV |
|------|-------------|-----------------------------|------------|
| 1 | \$1,000,000 | 1.109 | \$901,712 |
| 2 | \$1,200,000 | 1.229881 | \$975,920 |
| 3 | \$1,300,000 | 1.364057 | \$953,463 |
| 4 | \$900,000 | 1.513753 | \$594,674 |
| 5 | \$1,000,000 | 1.680348 | \$595,072 |
| | | | **\$4,020,841** |
---
**Note:** Rounded to the nearest dollar. If you need more decimal accuracy, keep more decimals in intermediate steps.
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