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Student question
Question
1
0
: What is the target debt to equity ratio of PXD wants a WACC of
1
2
%
?

PXD has a cost of equity capital of
1
5
%

Question

Hide student question
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Student question  
Question 
1
0
: What is the target debt to equity ratio of PXD wants a WACC of 
1
2
%
?
 
 ﻿PXD has a cost of equity capital of 
1
5
%
,
 ﻿their cost of debt before taxes is 
1
0
%
,
 ﻿and their tax rate is 
2
0
%
.

Answer to two decimal places, X
.
XX without a sign.

(
Note: Wd 
+
 ﻿We 
=
 
1
)
Question 
1
1
: MMM has 
1
0
0
,
0
0
0
 ﻿bonds outstanding that pay $
2
5
 ﻿every six months.
 
 ﻿The bonds currently sell for $
8
8
0
 ﻿and mature in 
5
 ﻿years.
 
 ﻿The U
.
S
.
 ﻿Treasury bill 
(
rf
)
 ﻿is yielding 
2
%
 ﻿and the expected market return is 
1
2
%
.
 
 ﻿What is MMM
'
s before
-
tax cost of debt capital?
 
 ﻿Answer in X
.
XX
%
 ﻿format without the percentage sign, so X
.
XX
.

(
Note: format your Excel answer to two decimal places to avoid rounding mistakes.
)
Question 
1
2
: CSLR has 
1
0
,
0
0
0
 ﻿shares of common stock outstanding at a market price of $
2
0
 ﻿a share.
 
 ﻿There are no shares of preferred stock outstanding.
 
 ﻿The tax rate is 
2
1
%
.
 
 ﻿The firm has a before tax cost of debt of 
5
%
,
 ﻿a cost of equity of 
1
3
%
,
 ﻿and a cost of preferred stock of 
8
%
.
 
 ﻿The bond issue ha

VIPSolutions · Accepted Answer

Let's answer each question step by step:

---

**Question 10: Target Debt-to-Equity Ratio for PXD (WACC = 12%)**

Given:  
- Cost of Equity ($r_e$) = 15%  
- Pre-tax Cost of Debt ($r_d$) = 10%  
- Tax Rate = 20%  
- WACC = 12%

**WACC Formula:**  
$ WACC = W_e \cdot r_e + W_d \cdot r_d \cdot (1-T) $  
Where:  
- $W_e$ = Weight of equity  
- $W_d$ = Weight of debt  
- $W_e + W_d = 1$

Let $W_d = x$, $W_e = 1 - x$

Set up equation:  
$ 0.12 = (1-x) \cdot 0.15 + x \cdot 0.10 \cdot (1-0.20) $  
$ 0.12 = 0.15 - 0.15x + 0.08x $  
$ 0.12 = 0.15 - 0.07x $  
$ 0.12 - 0.15 = -0.07x $  
$ -0.03 = -0.07x $  
$ x = \frac{-0.03}{-0.07} = 0.4286 $

- **Weight of Debt (Wd):** 0.43  
- **Weight of Equity (We):** 0.57

**Debt-to-Equity Ratio:**  
$ \text{D/E} = \frac{Wd}{We} = \frac{0.43}{0.57} = 0.754 $

**Final answer:**  
**0.75**

---

**Question 11: MMM's Before-tax Cost of Debt**

Given:  
- Bonds: 100,000 outstanding, $25 coupon every 6 months (so $50/year), 5 years to maturity  
- Price = $880  
- Face value = $1,000  
- Need to solve for YTM (yield to maturity)

This is a semiannual bond, so:  
- N = 10 periods (5 years × 2)
- PMT = $25  
- FV = $1,000  
- PV = -$880

**Using the bond price formula or a financial calculator/Excel:**

In Excel:  
`=RATE(10,25,-880,1000)*2`

Let's do it by hand (approximate):

Bond price = $ \sum_{t=1}^{10} \frac{25}{(1+r)^t} + \frac{1000}{(1+r)^{10}} = 880 $  
Try r = 3% per period (6% annual):  
- PV of coupons: $ 25 \times \frac{1-1/1.03^{10}}{0.03} = 25 \times 8.5302 = 213.26 $
- PV of principal: $ 1000/1.03^{10} = 744.09 $
- Total = 957.35 (too high)

Try r = 4% per period (8% annual):  
- Coupons: $ 25 \times 8.1109 = 202.77 $
- Principal: $ 1000 / 1.04^{10} = 675.56 $
- Total = 878.33 (very close to 880)

So, semiannual YTM ≈ 4%  
Annual YTM ≈ 8%

Try r = 4.05% per period (8.1% annual):  
- Coupons: $ 25 \times 8.0825 = 202.06 $
- Principal: $ 1000 / 1.0405^{10} = 672.80 $
- Total = 874.86

Try r = 3.95% per period (7.9% annual):  
- Coupons: $ 25 \times 8.1393 = 203.48 $
- Principal: $ 1000 / 1.0395^{10} = 678.27 $
- Total = 881.75 (just above 880)

So, YTM ≈ 3.98% per period × 2 = 7.96%

**Final answer:**  
**7.96**

---

**Question 12: WACC for CSLR**

Given:  
- Common shares: 10,000 × $20 = $200,000  
- Bonds: $50,000 face value, sells at face value, so $50,000  
- No preferred stock outstanding  
- Tax rate = 21%  
- Debt cost = 5% (before tax)  
- Equity cost = 13%

Find weights:  
- Equity: $200,000  
- Debt: $50,000  
- Total: $250,000

We = 200,000 / 250,000 = 0.80  
Wd = 50,000 / 250,000 = 0.20

WACC = We × Re + Wd × Rd × (1 – T)  
= 0.80 × 0.13 + 0.20 × 0.05 × (1 – 0.21)  
= 0.104 + 0.20 × 0.05 × 0.79  
= 0.104 + 0.0079  
= 0.1119 → **11.19**

**Final answer:**  
**11.19**

---

**Question 13: WAG's Cost of Equity (CAPM)**

Given:  
- Beta = 1.05  
- Rf = 2%  
- Market return = 10%

CAPM:  
Cost of equity = Rf + Beta × (Market – Rf)  
= 2% + 1.05 × (10% – 2%)  
= 2% + 1.05 × 8%  
= 2% + 8.4%  
= **10.40**

---

### **Summary of Answers**

1. **Question 10:** 0.75  
2. **Question 11:** 7.96  
3. **Question 12:** 11.19  
4. **Question 13:** 10.40

Let me know if you need a breakdown for any calculation!

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