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%

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

MRI Cost	1,500,000.00		CF0	1	2	3	4	5	IRR	9.14%
Salvage Value	50,000.00		-1,700,000.00	500,000.00	500,000.00	500,000.00	300,000.00	350,000.00
Working Capital	200,000.00
CF Yr 1-3	500,000.00
CF Yr 4-5	300,000.00

Answer 1

		Tax Rate =20%=0.2
		Before tax cost of debt =6%
	Cd	After tax Cost of debt =6*(1-0.2)	4.80%
		Required Return of equity
		R=Rf+Beta*(Rm-Rf)
		Rf=risk free rate=3%
		Beta=0.8
		Rm=Market return=9%
		R=3+0.8*(9-3)=	7.80%
	Ce	Cost of equity	7.80%
	Wd	Weight of debt in the capital	0.6
	We	Weight of Equity in the capital	0.4
		Weighted Average Cost of Capital(WACC) =Wd*Cd+We*Ce
		WACC=0.6*4.8+0.4*7.8=	6.00%
		Present Value of Cash Flow
		(Cash Flow)/((1+i)^N)
		i=discount rate=WACC=6%=0.06
		N=Year of cash flow
	N	Year	0	1	2	3	4	5
	a	Initial cash flow	(1,700,000.00)
	b	Annual Cash Flow		500,000.00	500,000.00	500,000.00	300,000.00	300,000.00
	c	Salvage Value						50,000.00
	d=a+b+c	Net Cash flow	(1,700,000.00)	500,000.00	500,000.00	500,000.00	300,000.00	350,000.00	SUM
	PV=d/(1.06^N)	Present Value of net cash flow	(1,700,000.00)	471698.11	444998.22	419809.64	237628.10	261540.36	135,674.43
		Net Present Value =Sum of PVs	135,674.43
		Recommendation:
		a. Yes as it adds 136k in value