---
title: "EPS and book value; \\$1,000,000 capital"
subject: "Project Engineering"
chapter: 6
key: "semester_7/project_engineering:eps-bv-dollar-1000000-4000-shares"
source: https://www.bctengineer.com/q/semester_7/project_engineering/eps-bv-dollar-1000000-4000-shares
site: BCT Engineering
---

# EPS and book value; \$1,000,000 capital

Project Engineering · Chapter 6: Introduction to Project Financing

- Asked in: 2072 Kartik
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/project_engineering/eps-bv-dollar-1000000-4000-shares
- Whole chapter: https://www.bctengineer.com/md/semester_7/project_engineering/chapter-6

## Question

A project has total capacity of \$1,000,000 which consists of 4,000 shares @ \$100; \$300,000 preference shares @ 18% interest; and remaining loan @ 15% interest. Earning before income and tax in a year is \$200,000. Compute the Earning per Share (EPS) and Book Value of Share, if tax rate is 20%.

## Short answer

Interest = $45,000; EBT = $155,000; tax (20%) = $31,000; EAT = $124,000; preference dividend = $54,000; earnings for equity = $70,000. EPS = $70,000 / 4,000 = $17.50. Book value per share = $400,000 / 4,000 = $100.00.

## Answer

#### Data

- Ordinary shares: 4,000 x \$100 = \$400,000
- Preference shares = \$300,000 at 18%
- Loan = 1,000,000 - 400,000 - 300,000 = \$300,000 at 15%
- EBIT = \$200,000; tax = 20%

#### EPS

$$
\begin{aligned}
\text{Interest} &= 300,000 \times 15\% = 45,000\\
\text{EBT} &= 200,000 - 45,000 = 155,000\\
\text{Tax} &= 20\% \times 155,000 = 31,000\\
\text{EAT} &= 155,000 - 31,000 = 124,000\\
\text{Preference dividend} &= 300,000 \times 18\% = 54,000\\
\text{Earnings for equity} &= 124,000 - 54,000 = 70,000\\
EPS &= \frac{70,000}{4,000} = 17.50
\end{aligned}
$$

#### Book value

Book value per share = net worth belonging to ordinary shareholders / number of ordinary shares. No reserves or retained earnings are given, so net worth equals the ordinary share capital (preference capital and loan are not part of it).

$$
BV = \frac{400,000}{4{,}000} = 100.00
$$

**Answer: EPS = \$17.50 per share; book value = \$100.00 per share.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is the loan amount found in this problem?
   A. Total capital minus ordinary shares minus preference shares = $300,000
   B. Total capital minus preference shares = $700,000
   C. EBIT minus interest = $155,000
   D. Ordinary shares minus preference shares = $100,000
   Answer: A. Loan is the remaining capital: 1,000,000 - 400,000 - 300,000 = $300,000. (Key point: Finding the loan amount)

2. Which sequence gives earnings available to ordinary shareholders?
   A. EBIT - tax - interest - preference dividend
   B. EBIT - interest, then tax on the result, then - preference dividend
   C. EBIT - preference dividend - interest - tax
   D. EBIT - tax, then - interest and preference dividend together
   Answer: B. Interest is deducted before tax (EBT), tax is charged on EBT to get EAT, and the preference dividend is paid out of EAT. (Key point: Order of deductions)

3. What is the EPS (EAT 124,000, preference dividend 54,000, 4,000 shares)?
   A. $31.00
   B. $17.50
   C. $13.50
   D. $31.00 + 13.50 = $44.50
   Answer: B. Earnings for equity = 124,000 - 54,000 = 70,000; divided by 4,000 shares gives $17.50. (Key point: EPS result)

4. Why is the book value per share $100 here?
   A. Preference capital is included in net worth, giving 700,000/4,000
   B. Net worth is only ordinary share capital of $400,000 since no reserves are given, divided by 4,000 shares
   C. It equals EPS divided by the tax rate
   D. Loan is added to net worth, giving 700,000/7,000
   Answer: B. Preference capital and loan are not part of ordinary shareholders' net worth, so BV = 400,000/4,000 = 100. (Key point: Book value of share)

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