Question

John is thinking to open a restaurant. He will run it only 1 year. Initial cost for opening a restaurant is 100k. Restaurant will generate EBIT of 200k at the end of year for sure. Risk-free rate is 5%. Tax rate is 35%.

1. (a) Suppose John’s current wealth is 20k. He can borrow money from a bank. Bank knows that his restaurant will generate EBIT of 200k at the end of year for sure.

   1. In this situation, would he want to open the restaurant? What is the value of his equity of the restaurant (at t=0) if he opens it? (0.8pt)

   2. If he opens the restaurant at t=0 and sell entire ownership of the restaurant to Peter at t=0, with what price can John sell the ownership? How much return did John make relative to his investment at t=0? (0.8pt)

2. (b) Suppose John has enough wealth to cover the initial cost of 100k. Assume that he can’t borrow money.

   1. In this situation, would he want to open the restaurant? What is the value of his equity of the restaurant (at t=0) if he opens it? (0.8pt)

   2. If he opens the restaurant at t=0 and sell entire ownership of the restaurant to Peter at t=0, with what price can John sell the ownership? How much return did John make relative to his initial investment at t=0? (0.8pt)

(c) Suppose John has enough wealth to cover the initial cost of 100k and opened the restaurant at t=0 by paying the initial cost with his own money. Then, he decided to lever up his restaurant. To do so, he borrowed 80k from a bank with interest rate of 5%. That 80k goes to John’s pocket.

a. What is his restaurant equity value now? (0.8pt)
b. What is his total wealth now (at t=0) including the debt proceed of 80k? (0.8pt) c. Was it a good decision relative to part.b.a? (0.8pt)

d. After levering-up, John decided to sell his equity to Mike. With what price, can John sell the ownership? How much return did John make relative to his initial investment at t=0? (0.8pt)

4. (d) Suppose John has enough wealth to cover the initial cost of 100k and opened the restaurant at t=0 by paying the initial cost with his own money. Then, he decided to lever up his restaurant. But he only wants to borrow with the risk-free rate, 5%. Bank knows that his restaurant will generate 200k at t=1 for sure.

   a. What is maximum amount of money John can borrow to lever-up his restaurant? (0.8pt)

   b. If he does borrow the maximum amount, what is value of his restaurant? What is equity value of restaurant? (0.8pt)

   c. How much money did John make relative to his initial investment by levering-up this way? How much return did John make relative to his initial investment? (0.8pt)

5. (e) Suppose John has 0 wealth. Bank knows that once his restaurant is open, it will generate 200k at

t=1 for sure.

1. What is maximum amount of money John can borrow from bank? (0.8pt)

2. Can he open the restaurant? (0.8pt)

3. If your answer to (e).b is yes, would he open the restaurant? (0.8pt)

4. Does his wealth increase by opening the restaurant at t=0 by borrowing the maximum amount of money? If so, how much does it increase? (0.8pt)

Answer 1

Part a)

EBIT = 200,000; Interest = borrowing*5% = 80,000*5% = 4,000;

EBT = EBIT-Interest = 200,000-4,000 = 196,000; Tax = EBT*35% = 196,000*35% = 68,600;

EAT = EBT-tax = 196,000-68,600 = 127,400;

Present value of EAT = EAT/(1+risk free rate) = 127,400/(1+0.05) = 127,400/1.05 = 121,333

Value of his equity of the restaurant (at t=0) if he opens it = Present value of EAT-Borrowings = 121,333-80,000 = 41,333.

Yes, he can open the restaurant because Value of his equity at t0 is more than investment.

Part b)

Tax = EBIT*35% = 200,000*35% = 70,000;

EAT = EBIT-tax = 200,000-70,000 = 130,000;

Present value of EAT = EAT/(1+risk free rate) = 130,000/(1+0.05) = 130,000/1.05 = 123,810

Value of his equity of the restaurant (at t=0) if he opens it = Present value of EAT = 123,810.

Yes, he can open the restaurant because Value of his equity at t0 is more than investment.

He can sell restaurant at minimum value of 123,810.

Return on initial investment = (Value of his equity of the restaurant - Initial investment)/Initial investment = (123,810-100,000)/100,000 = 23,810/100,000 = 23.81%

Part c)

EBIT = 200,000; Interest = borrowing*5% = 80,000*5% = 4,000;

EBT = EBIT-Interest = 200,000-4,000 = 196,000; Tax = EBT*35% = 196,000*35% = 68,600;

EAT = EBT-tax = 196,000-68,600 = 127,400;

Present value of EAT = EAT/(1+risk free rate) = 127,400/(1+0.05) = 127,400/1.05 = 121,333

Value of his equity of the restaurant (at t=0) if he opens it = Present value of EAT-Borrowings = 121,333-80,000 = 41,333.

Total wealth = Value of his equity of the restaurant+80000 = 41,333+80,000 = 121,333

With relation to part b it is not a good decision.

John can sell restaurant at minimum value of 41,333.

Return on initial investment = (Value of his equity of the restaurant+Loan proceed - Initial investment)/Initial investment = (41,333+80,000-100,000)/100,000 = 21,333/100,000 = 21.33%

Part d)

Tax = EBIT*35% = 200,000*35% = 70,000;

EAT = EBIT-tax = 200,000-70,000 = 130,000;

Present value of EAT = EAT/(1+risk free rate) = 130,000/(1+0.05) = 130,000/1.05 = 123,810

John can borrow entire initial cost of 100,000 as loan from bank because cashflow after 1year it can cover both principal & interest portion.

If john borrows entire 100,000 from bank then,

EBIT = 200,000; Interest = borrowing*5% = 100,000*5% = 5,000;

EBT = EBIT-Interest = 200,000-5,000 = 195,000; Tax = EBT*35% = 195,000*35% = 68,250;

EAT = EBT-tax = 195,000-68,250 = 126,750;

Present value of EAT = EAT/(1+risk free rate) = 126,750/(1+0.05) = 126,750/1.05 = 120,714

Value of his equity of the restaurant (at t=0) = Present value of EAT-Borrowings = 120,714 - 100,000 = 20,714.

John makes 100,000(borrowings) & 20,714 = 120,714 by making initial invetment.

Rate of return = 20,714/100,000 = 20.71%