Question

The Tomas School of Falconry is considering replacing a piece of equipment used in making falconry perches. The existing machine has 3 years useful life remaining. The machine had an original cost of $50,000, 3 years ago, and is projected to have a salvage value of $5,000 in 3 years time. The existing machine has a current market value of $30,000. The company has been depreciating the machine down to its salvage value using straight line depreciation. The new machine has a useful life of 3 years, will cost $75,000, and will be depreciated using the MACRS 3 year table (yr-1 33.33%, yr-2 44.44%, yr-3 14.82%, yr-4 7.41%). The new machine will have an expected salvage value of $8,000 in 3 years time. The new machine will save $40,000 a year in costs. There will be no change in Net Working Capital usage for the new machine versus the old machine. The company is in the 40% tax bracket. The Tomas School of Falconry has 12 million shares of stock outstanding with a current market price of $11.30. The stock’s beta is 2.3. The return on the S&P500 is expected to be 11%, while the return on 1 year Treasury bills is 2.2%. The company has $30 million in face value of debt outstanding. The debt has a price of 93’21. The bonds have a coupon rate of 7%, and pay coupons semi-annually. The bonds will mature in 25 years. Based on NPV should the School replace the existing machine?

Answer 1

First we will find the weighted average cost of capital to discount the cash flows :

Cost of equity

Given the details, we will find the cost of equity as per CAPM,

ie.ke=RFR+(Beta*Market risk premium)

where Market Risk Premium=Stock's Market return-Risk Free Rate

so, ke=2.2%+(2.3*(11%-2.2%))=

22.44%

Cost of bonds:

Using the formula to find the present value of bonds,

PV/Price of the bond=(Pmt.*(1-(1+r)^-n)/r)+(FV/(1+r)^n)

where price of the bond is given to be $ 93.21 per $ 100 FV

Pmt.= the semi-annual coupon pmt.= 7%/2*100= $ 3.5 per $ 100 FV

r= semi-annual yield /cost which we need to find--- ??

n= no.of semi-annual coupon periods= 25*2= 50

FV = Face value , which we are taking as $ 100

So, plugging in the values in the formula,

93.21=(3.5*(1-(1+r)^-50)/r)+(100/(1+r)^50)

& solving for r, we get the semi-annual before-tax yield/cost as

3.81%

Now the annual before-tax cost=(1+3.81%)^2-1=

7.77%

so, the annual after-tax cost=BT cost*(1-Tax Rate)

ie.7.77%*(1-40%)=

4.66%

Now, we have the cost of equity as 22.44% &

the cost of debt/bonds as 4.66%

we need to calculate the market value weights of equity & debt

Capital	Mkt.values		Wt.to Total	Cost	Wt.*Cost
Equity	12000000*11.30=	135600000	82.90%	22.44%	18.60%
Debt	30000000*93.21/100=	27963000	17.10%	4.66%	0.80%
Total		163563000	100.00%		19.40%
SO, WACC to discount the cash flows = 19.40%

NPV analysis of the Replacement decision:
Cost of new m/c	-75000
After-tax sale value of existing m/c(ref. wkgs.1)	29000
PV of after-tax savings in opg. Costs(40000*(1-40%)*2.12643)-----P/A,i=19.40%,n=3 yrs.	51034
PV of Incl. dep.tax shields(Ref. wkgs. 2)	12865
PV of after-tax sale(at end yr.6) of old m/c lost (-5000*(1-40%)/1.1940^3)	-1762
PV of after-tax salvage of new m/c(ref. wkgs.3)7023/1.194^3=	4126
NPV of the replacement decision	20263
As the NPV of the replacement decision is POSITIVE,it is RECOMMENDED to be replaced.

Workings:
1.After-tax Sale value of existing m/c
Cost 3 years ago	50000
Acc. Depn.(50000-5000)/6*3	22500
Carrying value,now	27500
Sale value,now	30000
Gain on sale	2500
Tax on gain	1000
so,After-tax sale cash flow for existing m/c	29000

	2.Annual depn.
Year	Existing m/c	New m/c		Incl.depn.	Incl.Tax shield on depn. At 40%	PV of incl. dep.tax sh. At 19.40%
1	7500	75000*33.33%=	24998	17498	6999	5861.81
2	7500	75000*44.44%=	33330	25830	10332	7247.29
3	7500	75000*14.82%%=	11115	3615	1446	849.48
4		75000*7.41%	-5558	-5558	-2223	-1093.76	####
						12864.82
####	Depn. Tax shield for yr. 4 lost due to sale at end of Yr. 3

3.After-tax Sale value of new m/c
Cost	75000
Acc. Depn.(75000*(33.33+44.44+14.82)%)	69443
Carrying value	5558
Sale value	8000
Gain on sale	2443
Tax on gain	977
so,After-tax sale cash flow for new m/c	7023