You have looked at the current financial statements for J&R Homes, Company.
The company has an EBIT of $3,650,000 this year. Depreciation, the increase
in net working capital, and capital spending w

Question

You have looked at the current financial statements for J&R Homes, Company.
The company has an EBIT of $3,650,000 this year. Depreciation, the increase
in net working capital, and capital spending were $265,000, $127,000, and
$515,000, respectively. You expect that over the next five years, EBIT will grow
at 18 percent per year, depreciation and capital spending will grow at 15 per
year, and NWC will grow at 20 per year. The company has $21,500,000 in debt
and 420,000 shares outstanding. After Year 5, the adjusted cash flow from
assets is expected to grow at 3.2 percent, indefinitely. The company’s WACC is
9.25 percent and the tax rate is 24 percent. What is the price per share of the
company's stock?

Note: Do not round intermediate calculations and round your answer to 2
decimal places, e.g., 32.16.

VIPSolutions · Accepted Answer

Let's break down the problem step by step.

### **Step 1: Calculate Free Cash Flow (FCF) for Year 1**
Given:
- EBIT = $3,650,000
- Depreciation = $265,000
- Increase in NWC = $127,000
- Capital Spending = $515,000
- Tax rate = 24%

$$
\text{FCF} = (\text{EBIT} \times (1 - \text{Tax rate})) + \text{Depreciation} - \text{Capital Spending} - \text{Increase in NWC}
$$

$$
\text{FCF}_1 = (3,650,000 \times (1-0.24)) + 265,000 - 515,000 - 127,000
$$
$$
= (3,650,000 \times 0.76) + 265,000 - 515,000 - 127,000
$$
$$
= 2,774,000 + 265,000 - 515,000 - 127,000
$$
$$
= 3,039,000 - 515,000 - 127,000
$$
$$
= 2,524,000 - 127,000
$$
$$
= 2,397,000
$$

### **Step 2: Project FCF for Years 1-5**
Growth rates:
- EBIT: +18%/year
- Depreciation & CapEx: +15%/year
- NWC: +20%/year

Let’s denote:
- EBIT in year $ t $: $ EBIT_1 \times (1.18)^{t-1} $
- Depreciation in year $ t $: $ Dep_1 \times (1.15)^{t-1} $
- CapEx in year $ t $: $ CapEx_1 \times (1.15)^{t-1} $
- NWC in year $ t $: $ NWC_1 \times (1.20)^{t-1} $

Let’s calculate FCF for each year:

#### **Year 1** (already calculated): $ \$2,397,000 $

#### **Year 2:**
$$
\text{EBIT}_2 = 3,650,000 \times 1.18 = 4,307,000
$$
$$
\text{Dep}_2 = 265,000 \times 1.15 = 304,750
$$
$$
\text{CapEx}_2 = 515,000 \times 1.15 = 592,250
$$
$$
\text{NWC}_2 = 127,000 \times 1.20 = 152,400
$$

$$
\text{FCF}_2 = (4,307,000 \times 0.76) + 304,750 - 592,250 - 152,400
$$
$$
= 3,274,520 + 304,750 - 592,250 - 152,400
$$
$$
= 3,579,270 - 592,250 - 152,400
$$
$$
= 2,987,020 - 152,400
$$
$$
= 2,834,620
$$

#### **Year 3:**
$$
\text{EBIT}_3 = 4,307,000 \times 1.18 = 5,083,260
$$
$$
\text{Dep}_3 = 304,750 \times 1.15 = 350,462.5
$$
$$
\text{CapEx}_3 = 592,250 \times 1.15 = 681,087.5
$$
$$
\text{NWC}_3 = 152,400 \times 1.20 = 182,880
$$

$$
\text{FCF}_3 = (5,083,260 \times 0.76) + 350,462.5 - 681,087.5 - 182,880
$$
$$
= 3,864,277.6 + 350,462.5 - 681,087.5 - 182,880
$$
$$
= 4,214,740.1 - 681,087.5 - 182,880
$$
$$
= 3,533,652.6 - 182,880
$$
$$
= 3,350,772.6
$$

#### **Year 4:**
$$
\text{EBIT}_4 = 5,083,260 \times 1.18 = 5,999,447
$$
$$
\text{Dep}_4 = 350,462.5 \times 1.15 = 403,032.9
$$
$$
\text{CapEx}_4 = 681,087.5 \times 1.15 = 783,250.6
$$
$$
\text{NWC}_4 = 182,880 \times 1.20 = 219,456
$$

$$
\text{FCF}_4 = (5,999,447 \times 0.76) + 403,032.9 - 783,250.6 - 219,456
$$
$$
= 4,559,579.7 + 403,032.9 - 783,250.6 - 219,456
$$
$$
= 4,962,612.6 - 783,250.6 - 219,456
$$
$$
= 4,179,362 - 219,456
$$
$$
= 3,959,906
$$

#### **Year 5:**
$$
\text{EBIT}_5 = 5,999,447 \times 1.18 = 7,079,349.5
$$
$$
\text{Dep}_5 = 403,032.9 \times 1.15 = 463,487.8
$$
$$
\text{CapEx}_5 = 783,250.6 \times 1.15 = 900,738.2
$$
$$
\text{NWC}_5 = 219,456 \times 1.20 = 263,347.2
$$

$$
\text{FCF}_5 = (7,079,349.5 \times 0.76) + 463,487.8 - 900,738.2 - 263,347.2
$$
$$
= 5,382,305.6 + 463,487.8 - 900,738.2 - 263,347.2
$$
$$
= 5,845,793.4 - 900,738.2 - 263,347.2
$$
$$
= 4,945,055.2 - 263,347.2
$$
$$
= 4,681,708
$$

---

### **Step 3: Calculate Terminal Value at Year 5**
After Year 5, FCF grows at 3.2% **indefinitely**.

$$
\text{TV}_5 = \frac{\text{FCF}_6}{WACC - g} = \frac{\text{FCF}_5 \times (1 + g)}{WACC - g}
$$

Where,
- $ g = 3.2\% $
- $ WACC = 9.25\% $
- $ \text{FCF}_5 = \$4,681,708 $

$$
\text{TV}_5 = \frac{4,681,708 \times 1.032}{0.0925 - 0.032}
$$
$$
= \frac{4,831,545}{0.0605}
$$
$$
= 79,884,297.52
$$

---

### **Step 4: Discount FCFs and Terminal Value to Present Value**

$$
PV = \sum_{t=1}^{5} \frac{FCF_t}{(1+WACC)^t} + \frac{TV_5}{(1+WACC)^5}
$$

#### Calculate Discount Factors:

- $ (1.0925)^1 = 1.0925 $
- $ (1.0925)^2 = 1.19357 $
- $ (1.0925)^3 = 1.30252 $
- $ (1.0925)^4 = 1.41996 $
- $ (1.0925)^5 = 1.54636 $

#### Discount FCFs:

- Year 1: $ \frac{2,397,000}{1.0925} = 2,194,061.51 $
- Year 2: $ \frac{2,834,620}{1.19357} = 2,376,299.49 $
- Year 3: $ \frac{3,350,772.6}{1.30252} = 2,572,246.28 $
- Year 4: $ \frac{3,959,906}{1.41996} = 2,788,883.73 $
- Year 5: $ \frac{4,681,708}{1.54636} = 3,027,082.31 $

Sum = 2,194,061.51 + 2,376,299.49 + 2,572,246.28 + 2,788,883.73 + 3,027,082.31 = **12,958,573.32**

#### Discount Terminal Value:

$$
\frac{79,884,297.52}{1.54636} = 51,676,481.63
$$

#### Total Firm Value:

$$
\text{Total PV} = 12,958,573.32 + 51,676,481.63 = 64,635,054.95
$$

---

### **Step 5: Subtract Debt to get Equity Value**

$$
\text{Equity Value} = 64,635,054.95 - 21,500,000 = 43,135,054.95
$$

---

### **Step 6: Divide by Shares Outstanding**

$$
\text{Share Price} = \frac{43,135,054.95}{420,000} = 102.70
$$

---

## **Final Answer**

$$
\boxed{102.70}
$$

**The price per share of the company's stock is \$102.70.**

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