Question

You just got hired at a brand new hospital as a financial analyst and the Board wants to buy an MRI machine but they are unsure if this makes financial sense. You gather some figures so you can make an informed decision to present to the Board. (questions 40-44) Use CF’s given, no further calculation has to be done for CF’s.

Cost of the MRI machine 1.5 million

Salvage value after 5 years 50k

Working capital to hire an operator 200k only initially and not recoverable.

CF yr 1-3 400k

CF yr 4-5 300k

The hospital currently has no common stock or preferred stock or debt in their capital structure as it was funded with a 25 million dollar gift from Bill Gates. The machine is to be financed with a 5%, 5 year loan. Interest is tax deductible and the tax rate is 30%.

40. The IRR on this MRI machine is:

1. 4%
2. 3%
3. 7.7%
4. 6.8%

41. T/F Based on the IRR decision criteria we should accept this project

42. Based on the NPV analysis what should you recommend to the board

a. Do not recommend as it will take away 89k of value

b. Recommend as it will add 135k in value

c. Recommend as it will add 177k in value

d. Do not recommend as it will take away 23k of value

43. Assume now that the hospital was financed with 60% debt and 40% equity. The cost of debt is 6% and taxes are 20%, while the risk free rate is 3%, beta is .8 and the return of the market is 9%. If cash flow in years 1-3 are now assumed to increase to 500k instead of 400k, what would you recommend to the board?

a. Yes as it adds 136k in value

b. Yes as it adds 98k in value

c. no as the IRR

d. Yes as it adds 100k in value

44. T/F the payback under the original MRI assumptions is 4.67 years

Answer 1

First, I have provided al the answers and then the workings and explanations.

Q - 40. The IRR on this MRI machine is: The correct answer is option b. 3%

Q - 41 T/F Based on the IRR decision criteria we should accept this project.

IRR = 3%, Cost of capital = Pre tax cost of debt x (1 - tax rate) = 5% x (1 - 30%) = 3.5%

Since, IRR < Cost of capital, we should not accept this project. Hence the statement is FALSE.

Q - 42

Based on the NPV analysis what should you recommend to the board:

The correct answer is option d. Do not recommend as it will take away 23k of value.

Please see the NPV calculation below.

Q - 43: I have answered it after Q - 44

Q - 44: T/F the payback under the original MRI assumptions is 4.67 years.

The statement is TRUE. Please see the payback calculation in the table below.

Excel working for Q - 40, 41, 42 & 44.

Please see the table below. Please be guided by the second column titled “Linkage” to understand the mathematics. The last few rows highlighted in yellow contain your answer. Figures in parenthesis, if any, mean negative values. All financials are in $. Adjacent cells in blue contain the formula in excel I have used to get the final output.

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Q - 43

The correct answer is option a. Yes as it adds 136k in value

Proportion of debt, Wd = 60% debt

Proportion of equity, We = 40% equity.

Pre tax cost of debt = Kd = 6%

Tax rate = 20%,

the risk free rate, Rf = 3%,

beta = 0.8 and

the return of the market, Rm = 9%. If cash flow in years 1-3 are now assumed to increase to 500k instead of 400k,

Cost of equity, Ke = Rf + beta x (Rm - Rf) = 3% + 0.8 x (9% - 3%) = 7.8%

WACC = Wd x Kd x (1 - T) + We x Ke = 60% x 6% x (1 - 20%) + 40% x 7.8% = 6.00%

Please see the NPV calculation below:

NPV is now $ 135,674 ~ $ 136 k