Problem 13-3 ROE and Leverage [LO 1, 2] Kaelea, Inc., has no debt outstanding an
ID: 2755964 • Letter: P
Question
Problem 13-3 ROE and Leverage [LO 1, 2] Kaelea, Inc., has no debt outstanding and a total market value of $129,000. Earnings before interest and taxes, EBIT, are projected to be $8,700 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 22 percent higher. If there is a recession, then EBIT will be 33 percent lower. Kaelea is considering a $42,900 debt issue with an interest rate of 5 percent. The proceeds will be used to repurchase shares of stock. There are currently 4,300 shares outstanding. Assume Kaelea has a market-to-book ratio of 1.0. Requirement 1: (a) Calculate return on equity, ROE, under each of the three economic scenarios before any debt is issued, assuming no taxes. (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) ROE Recession % Normal % Expansion % (b) Calculate the percentage changes in ROE when the economy expands or enters a recession, assuming no taxes. (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign.) %ROE Recession -33 % Expansion 22 % Requirement 2: Assume the firm goes through with the proposed recapitalization and no taxes. (a) Calculate return on equity, ROE, under each of the three economic scenarios after the recapitalization. (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) ROE Recession % Normal % Expansion % (b) Calculate the percentage changes in ROE for economic expansion and recession. (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) %ROE Recession -43.80 % Expansion 29.20 % Requirement 3: Assume the firm has a tax rate of 40 percent. (a) Calculate return on equity, ROE, under each of the three economic scenarios before any debt is issued. Also, calculate the percentage changes in ROE for economic expansion and recession. (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) ROE Recession % Normal % Expansion % %ROE Recession -33 % Expansion 22 % (b) Calculate return on equity, ROE, under each of the three economic scenarios after the recapitalization. Also, calculate the percentage changes in ROE for economic expansion and recession, assuming the firm goes through with the proposed recapitalization. (Do not round intermediate calculations Negative amounts should be indicated by a minus sign. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) ROE Recession % Normal % Expansion % %ROE Recession % Expansion %
Explanation / Answer
Requirement 1
Answer:(a) &(b)
a. Since the company has a market-to-book ratio of 1.0, the total equity of the firm is equal to the market value of equity. Using the equation for ROE:
ROE = NI/$129,000
The ROE for each state of the economy under the current capital structure and no taxes is:
Recession
Normal
Expansion
ROE
.0452
.06744
.0822
%DROE
–33
–––
+22
The second row shows the percentage change in ROE from the normal economy.
Requirement 2
Answer:(a) & (b)
If the company undertakes the proposed recapitalization, the new equity value will be:
Equity = $129,000 – 42900
Equity = $86100
So, the ROE for each state of the economy is:
ROE = NI/$86100
Recession
Normal
Expansion
ROE
.04278
.07613
.09836
%DROE
–43.80
–––
+29.20
Requirement 3:
Answer:
Recession
Normal
Expansion
EBIT
$5829
$8700
$10614
Interest
0
0
0
Taxes @ 40%
$ 2332
$3480
$4246
Net Income
$3497
$5220
$6368
ROE
0.02711
0.04046
0.04936
% Change in ROE
-32.99%
-
21.99%
Recession
Normal
Expansion
EBIT
$5829
$8700
$10614
Interest
2145
2145
2145
EBT
3684
6555
8469
Taxes @ 40%
$ 1474
$2622
$3388
Net Income
$2210
3933
$5081
ROE
0.02567
0.04568
0.0590
% Change in ROE
-43.80%
-
29.16%
Recession
Normal
Expansion
ROE
.0452
.06744
.0822
%DROE
–33
–––
+22