1)Option A is the answer.

if we discount the 5000 to the year zero then the value will be

From Year 0 to year 5.

Present Value= FutureValue/(1+rate)^t

= 5000/(1.07^5)

= 3564.93=X

discount from year 10 to year 5.

PV = 5000/(1.07^5)

= 3564.93=Y

|X-Y| = 0

Option (A) is the correct ans.

2)

Let i be the interest rate

Interest during the last 6 months of the 10th year

A₁₀ -A_9.5 = A_9.5(1+i/2) - A_9.5 = A_9.5* i/2

A_{9.5 *i/2}=

During last 6 months Simple interest earned =

As the interest earned is same

i = 7.4%

Ans B)7.4%

please see the attached file.

3)

First we find t. Since the amounts are equal,

25000 x (1 + 0.05t) = X x (1.02)^t

Since the annual interest rate is same, we have

0.05 x 25000/(25000 x (1+0.5(t-1)) = 0.02

62500 = 25000 + 12500(t - 1)

37500/12500 = t - 1

t = 4

Now, solving for X

30000/1.02^4 = X

X = 25256

Option A is correct.

4)

Answer 1:

Scenario 1 - Normal Condition

EBIT = $52000, Market cap = $382,500

As there is no debt, Market cap = Total equity

ROE = Net income / Equity

Now, there is no debt, hence interest = 0 and taxes are to be ignored as given in the problem

Hence, Net income = EBIT

ROE = EBIT / Market cap

= 52000 / 382500

Hence, ROE = 13.59%

Scenario 2 - Expansion in economy

EBIT will increase by 14%

So, EBIT = 1.14 * $52000 = $59280

ROE = 59280 / 382500

Hence, ROE = 15.49%

Scenario 3 - Depression in economy

EBIT will decrease by 23%

So, EBIT = 0.77 * $52000 = $40040

ROE = 40040 / 382500

Hence, ROE = 10.46%

Answer 2:

Change in ROE in expansion = (15.49 - 13.59) / 13.59 * 100 = +13.98%

Change in ROE in depression = (10.46 - 13.59) / 13.59 *100 = -23.03%

Answer 3:

Company is considering $190000 debt with 7% interest

Hence, interest = 0.07 * $190000 = $13300

Net income = EBIT - interest - taxes = $52000 - $13300 = $38700

Equity = Market cap - debt = $382,500 - $190,000 = $192,500

Scenario 1 - Normal condition

ROE = Net income / Equity

= 38700 / 192500

Hence, ROE = 20.10%

Scenario 2 - Expansion in economy

EBIT = $59280

Net income = EBIT - interest - taxes = $59280 - $13300 = $45980

ROE = 45980 / 192500

Hence, ROE = 23.88%

Scenario 3 - Depression in economy

EBIT = $40040

Net income = EBIT - interest - taxes = $40040 - $13300 = $26740

ROE = 26740 / 192500

Hence, ROE = 13.89%

Answer 4:

Change in ROE in expansion = (23.88 - 20.10) / 20.10 * 100 = +18.80%

Change in ROE in depression = (13.89 - 20.10) / 20.10 *100 = -30.89%