Question

You are considering replacing a current machine with a new machine that has an 8-year life. The purchase price of the new machine is $635,000 and transportation/installation expenses will be $100,000. This new machine falls into the 5-year MACRS classification for depreciation purposes. At the end of that 8-year life of the new machine, it is expected to have a market value of $260,000. The current equipment has been in use for 7 years and has an expected remaining life of 8 years. Seven years ago, you purchased the equipment for a total of $480,000. This current equipment is being depreciated on a straight-line basis to an expected zero salvage value for accounting purposes. You estimate the market value of the equipment to be $264,000 currently and $127,000 at the end of 8 years. You estimate that inventories will increase by $58,000 and accounts receivable will increase by $65,000 with the purchase of the new equipment. If you continue to operate the old machine, you estimate that you can produce and sell 124,000 units per year at the current price of $6 per unit. Variable costs currently associated with running the old machine are $1.93 per unit, and fixed costs associated with the old machine are currently $118,500 annually. If you switch to the new machine, you anticipate that you can produce and sell 142,500 units at a beginning price of $8 per unit. Variable costs associated with running the new machine are estimated to be $2.75 per unit to start, while estimated fixed costs are $130,425 in the first year. Assume that the unit selling price, annual variable costs, and annual fixed costs for both the current and new machine under consideration will grow at a 1.0% annual rate of inflation beginning in year two of your analysis. Depreciation for Tax Purposes: Modified Accelerated Cost Recovery System (MACRS) Ownership Year 5-year 1 20% 2 32% 3 19% 4 11.5% 5 11.5% 6 6% Your firm is financed with debt and common equity. Debt is comprised of a single issue of 2,000 bonds that are currently trading at a price of $1,025 each. The bonds were issued exactly two years ago today, each with a par value of $1,000, a coupon rate of 4.5%, and total maturity of 30 years. Interest coupons are paid on a semi-annual basis. For common equity, there are currently 253,000 shares outstanding, trading at a price of $13.75 each. Dividends are paid on an annual basis, and the last dividend paid was $1.70 per share. Dividends are expected to grow at a rate of 3% for the foreseeable future. You have chosen to use an historical market risk premium estimate of 6%. It is your firm’s policy to use the current yield of 0.50% on 5-year T-bonds as your proxy for the nominal risk-free rate of return. Finally, you believe the estimated levered equity beta of your firm is 2.40. You determine that the current market value of your firm’s capital structure approximates the target capital structure and that the risk of the project under consideration is comparable to the overall risk level of the firm’s existing asset mix. Also, if there is more than one way to estimate a variable, it is your firm’s policy to use the average of the estimations. Assume that your firm’s marginal tax rate is 50%.   Base Case Question 1.1 (20 points): Estimate the weighted average cost of capital (WACC) that should be used in analyzing the decision to replace the old piece of equipment with the new one under consideration. Base Case Question 1.2 (40 points): Should you replace the old piece of equipment with the new one under consideration? Substantiate your answer using NPV, IRR, and MIRR.

Answer 1

Part 1.1

Return on equity = Levered equity beta * Market risk premium + Risk-free rate of return

= 2.4*6% + 0.5% = 14.4% + 0.5% = 14.9%

Calculation of WACC

Type (1)	Rate of return (after tax) (2)	Market value (3)	Propotion based on market value (4)	WACC (5)=(2*4)
Debt	4.5%*(1-0.5) = 2.25%	2000*1025 = 20,50,000	0.3708	0.83%
Equity	14.90%	253000*13.75 = 34,78,750	0.6292	9.38%
		55,28,750	1.0000	10.21%

Part 1.2)- New machine gives NPV more than old machine whereas IRR & MIRR of new machine is less than old machine. If u have return from other projects more than IRR of new machine invest in that project else use new machine & generate more NPV.

Purchase price of new machine = $635,000 ; Transportation expenses = $100,000

Total amount to be depreiated = $635,000 + $100,000 = $735,000

Depreciation for year 1=$735,000*20%=$147,000; Depreciation for year 2=$735,000*32%=$235,200

Depreciation for year 3=$735,000*19%=$139,650; Depreciation for year 4=$735,000*11.5%=$84,525

Depreciation for year 5=$735,000*11.5%=$84,525; Depreciation for year 6=$735,000*6%=$44,100

Depreciation for old machine=$480,000/15years =$32,000 per year

Book value of old machine at the end of year 7 =$480,000 - ($32,000*7) =$480,000 - $224,000 =$256,000

Note : Assume additional working capital will not be realised at the end of the project. Book value of old machine is allowed for tax dedution purpose.

NPV by using old machine = $898,212
Serial No	Particulars	t=0	t=1	t=2	t=3	t=4	t=5	t=6	t=7	t=8
1	Revenue from sales		$    744,000	$   751,440	$   758,954	$   766,544	$      774,209	$   781,951	$   789,771	$   797,669
2	Variable cost		$   -239,320	$ -241,713	$ -244,130	$ -246,572	$     -249,037	$ -251,528	$ -254,043	$ -256,583
3	Fixed costs		$   -118,500	$ -119,685	$ -120,882	$ -122,091	$     -123,312	$ -124,545	$ -125,790	$ -127,048
4	Interest on bond		$    -90,000	$   -90,000	$   -90,000	$   -90,000	$       -90,000	$   -90,000	$   -90,000	$   -90,000
5	Proceed from sale of existing machine									$   127,000
6	EBITDA		$    296,180	$   300,042	$   303,942	$   307,882	$      311,860	$   315,879	$   319,938	$   451,037
7	Depreciation		$    -32,000	$   -32,000	$   -32,000	$   -32,000	$       -32,000	$   -32,000	$   -32,000	$   -32,000
8	EBIT		$    264,180	$   268,042	$   271,942	$   275,882	$      279,860	$   283,879	$   287,938	$   419,037
9	Tax expenses @ 50%		$   -132,090	$ -134,021	$ -135,971	$ -137,941	$     -139,930	$ -141,940	$ -143,969	$ -209,519
10	NOPAT		$    132,090	$   134,021	$   135,971	$   137,941	$      139,930	$   141,940	$   143,969	$   209,519
11	Depreciation		$      32,000	$    32,000	$    32,000	$     32,000	$        32,000	$    32,000
12	Operating cashflow		$    164,090	$   166,021	$   167,971	$   169,941	$      171,930	$   173,940	$   143,969	$   209,519
13	Present value factor @ 10.21%	1.0000	0.9074	0.8233	0.7470	0.6778	0.6150	0.5581	0.5064	0.4594
14	Discounted cash flow		$    148,888	$   136,685	$   125,479	$   115,190	$      105,742	$    97,067	$    72,899	$    96,262

New Machine	Old Machine
Year	Cashflow	Year	Cashflow
0	$-598,000	0	$-264,000
1	$ 337,350	1	$ 164,090
2	$ 384,539	2	$ 166,021
3	$ 339,883	3	$ 167,971
4	$ 315,471	4	$ 169,941
5	$ 318,653	5	$ 171,930
6	$ 301,654	6	$ 173,940
7	$ 282,850	7	$ 143,969
8	$ 416,129	8	$   209,519
IRR	56%	IRR	62%
MIRR	30%	MIRR	32%

Required rate of return=Expected Dividend/Market price+growth rate

where, Growth rate=3%;expected dividend=$1.7*(1+0.03)=$1.751 Market price=$13.75

Required ROR/Reinvestment rate = 1.751/13.75 + 3% =12.73%+3% =15.73%