Please solve the table and part B
.

Slinger

Wayne, a

U
.
S
.
-
based private equity

firm, is trying to determine what it should pay for a tool manufacturing firm in Hondura

Question

Please solve the table and part B
.
 
Slinger
​
 ﻿Wayne, a
​
 ﻿U
.
S
.
-
based private equity
​
 ﻿firm, is trying to determine what it should pay for a tool manufacturing firm in Honduras named Carambola. Slinger Wayne estimates that Carambola will generate a free cash flow of
1
4
million Honduran lempiras
​
 
(
Lp
)
 ﻿next year
​
 
(
2
0
2
2
)
,
 ﻿and that this free cash flow will continue to grow at a constant rate of
7
.
5
​
%
per annum indefinitely.
A private equity firm like Slinger
​
 ﻿Wayne, however, is not interested in owning a company for
​
 ﻿long, and plans to sell Carambola at the end of three years for approximately 
1
0
 ﻿times
​
 ﻿Carambola's free cash flow in that year. The current spot exchange rate is
Lp
2
3
.
5
6
​
=
 ﻿$
1
.
0
0
,
 ﻿but the Honduran inflation rate is expected to remain at a relatively high rate of
1
4
.
5
​
%
per annum compared to the U
.
S
.
 ﻿dollar inflation rate of only
1
.
5
​
%
per annum. Slinger Wayne expects to earn at least a
 
 
2
2
.
5
%
annual rate of return on international investments like Carambola.
a
.
 ﻿What is Carambola worth if the Hondu

VIPSolutions · Accepted Answer

Let's solve **Part A** step by step using the information given:

### 1. **Calculate Free Cash Flows (FCF) in Lempiras (Lp)**
- Year 1 FCF = Lp 14,000,000
- Growth rate (g) = 7.5% per year

#### Calculate FCF for Years 2 and 3:
- Year 2 FCF = Year 1 FCF × (1 + g)  
  = 14,000,000 × 1.075 = **Lp 15,050,000**
- Year 3 FCF = Year 2 FCF × (1 + g)  
  = 15,050,000 × 1.075 = **Lp 16,176,250**

### 2. **Expected Sale Value in Year 3**
- Sale value = 10 × Year 3 FCF  
  = 10 × 16,176,250 = **Lp 161,762,500**

### 3. **Total Expected Cash Flow in Each Year**
- Year 1: FCF only = **Lp 14,000,000**
- Year 2: FCF only = **Lp 15,050,000**
- Year 3: FCF + Sale value = 16,176,250 + 161,762,500 = **Lp 177,938,750**

### 4. **Exchange Rate**
- Lp 23.56 = $1.00 (fixed over 3 years)

---

#### **Fill in the Table**

| Year     | Year 1      | Year 2      | Year 3         |
|----------|-------------|-------------|----------------|
| Carambola's expected free cash flow | 14,000,000 | 15,050,000 | 16,176,250 |
| Expected sale value in year 3       |             |             | 161,762,500|
| Total expected cash flow            | 14,000,000 | 15,050,000 | 177,938,750|
| Expected exchange rate (Lp/$)       | 23.5600     | 23.5600     | 23.5600    |

---

### 5. **Carambola's expected cash flow in US$**
Divide each year's total expected cash flow by the exchange rate:

- Year 1: 14,000,000 / 23.56 ≈ **$594,615**
- Year 2: 15,050,000 / 23.56 ≈ **$639,244**
- Year 3: 177,938,750 / 23.56 ≈ **$7,557,776**

---

## **Summary Table (Filled):**

| Year     | Year 1      | Year 2      | Year 3         |
|----------|-------------|-------------|----------------|
| Carambola's expected free cash flow | 14,000,000 | 15,050,000 | 16,176,250 |
| Expected sale value in year 3       |             |             | 161,762,500|
| Total expected cash flow            | 14,000,000 | 15,050,000 | 177,938,750|
| Expected exchange rate (Lp/$)       | 23.5600     | 23.5600     | 23.5600    |
| Carambola's expected cash flow in US$ | 594,615   | 639,244    | 7,557,776  |

---

## **Next Steps (Part a, Continued)**

### **Calculate Present Value (PV) in USD**
Discount the USD cash flows at the required return (22.5%):

- PV = CF / (1 + r)^n

- Year 1: 594,615 / (1.225^1) = 485,233  
- Year 2: 639,244 / (1.225^2) = 426,944  
- Year 3: 7,557,776 / (1.225^3) = 4,028,377

- **Total PV ≈ $4,940,554**

---

## **Part B: Effect of PPP (Purchasing Power Parity)**

PPP implies the Lempira will depreciate relative to the USD by the inflation differential.

### 1. **Expected Depreciation Rate**
- Honduras inflation = 14.5%
- US inflation = 1.5%
- Expected annual depreciation ≈ 14.5% - 1.5% = **13% per year**

### 2. **Expected Exchange Rate in Future Years**

- Year 1: 23.56 × 1.13 = **26.623**
- Year 2: 26.623 × 1.13 ≈ **30.084**
- Year 3: 30.084 × 1.13 ≈ **34.995**

### 3. **Calculate USD Cash Flows Using PPP-adjusted Exchange Rates**

- Year 1: 14,000,000 / 26.623 ≈ **$525,803**
- Year 2: 15,050,000 / 30.084 ≈ **$500,287**
- Year 3: 177,938,750 / 34.995 ≈ **$5,085,597**

### 4. **Present Value (Same Discount Rate, 22.5%)**

- Year 1: 525,803 / 1.225 = 429,222
- Year 2: 500,287 / (1.225^2) = 333,646
- Year 3: 5,085,597 / (1.225^3) = 3,155,590

- **Total PV ≈ $3,918,458**

---

## **Summary of Answers**

### **a. If the Lempira were fixed:**  
**Carambola is worth ≈ $4,940,554**

### **b. If the Lempira depreciates by PPP:**  
**Carambola is worth ≈ $3,918,458**

---

**If you need these answers in table format for submission, let me know!**

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