1 Mr Art Deco will be paid $100,000 one year hence This is a nominal flow, which he discounts at a nominal discount rate of 8 PV $100,000 (1 08) $92,593 The inflation rate is 4 Calculate the PV of Mr Decos payment using the equivalentrealcash flow andrealdiscount rate (You should get exactly the same answer as he did ) Real cash flow $ Real discount rate Present value 2 Machines A and B are mutually exclusive and are expected to produce the following real cash flows Cash Flows ($ thousands) Machine C 0 C 1 C 2 C 3 A 100 110 121 B 120 110 121 133 The real opportunity cost of capital is 10 a Calculate the NPV of each machine Machine A NPV Machine B NPV b Calculate the equivalent annual cash flow from each machine Machine A $ Machine B $ 3 ($ thousands) Period 0 1 2 3 4 5 6 7 Net cash flow 12,600 1,484 2,947 6,323 10,534 9,985 5,757 3,269 Present value at 20 12,600 1,237 2,047 3,659 5,080 4,013 1,928 912 Net present value 3,802 (sum of PVs) Restate the above net cash flows in real terms Discount the restated cash flows at a real discount rate Assume a 20 nominalrate and 10 expected inflation NPV should be unchanged at 3,802, or $3,802,000 Fill in the net cash flows for year 0 7 and the NPV at year 0 Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Net cash flows (real) Net present value $ 4 a result of improvements in product engineering, United Automation is able to sell one of its two milling machines Both machines perform the same function but differ in age The newer machine could be sold today for $50,000 Its operating costs are $20,000 a year, but in five years the machine will require a $20,000 overhaul Thereafter operating costs will be $30,000 until the machine is finally sold in year 10 for $5,000 The older machine could be sold today for $25,000 If it is kept, it will need an immediate $20,000 overhaul Thereafter operating costs will be $30,000 a year until the machine is finally sold in year 5 for $5,000 Both machines are fully depreciated for tax purposes The company pays tax at 35 Cash flows have been forecasted in real terms The real cost of capital is 12 a Calculate the equivalent annual costs for selling the new machine and for selling the old machine (Do not round intermediate calculations Enter your answers as a positive value rounded to 2 decimal places ) Equivalent Annual Cost Sell new machine $ Sell old machine 5 Low energy lightbulbs typically cost $3 60, have a life of nine years, and use about $2 00 of electricity a year Conventional lightbulbs are cheaper to buy, for they cost only $ 60 On the other hand, they last only about a year and use about $7 00 of energy a If the real discount rate is 4 , what is the equivalent annual cost of the two products (Do not round intermediate calculations Enter your answers as a positive value rounded to 2 decimal places ) Equivalent Annual Cost Low energy lightbulbs $ Conventional lightbulbs 6 The Borstal Company has to choose between two machines that do the same job but have different lives The two machines have the following costs Year Machine A Machine B 0 $40,000 $50,000 1 10,000 8,000 2 10,000 8,000 3 10,000 replace 8,000 4 8,000 replace These costs are expressed in real terms a Suppose you are Borstals financial manager If you had to buy one or the other machine and rent it to the production manager for that machines economic life, what annual rental payment would you have to charge Assume a 6 real discount rate and ignore taxes (Do not round intermediate calculations Enter your answers as a positive value rounded to 2 decimal places ) Annual Rental Payment Machine A $ Machine B b If there is steady 8 per year inflation, what will be the annual rental payment for machine B for the second year Year 2 rental payment 7 Ms T Potts, the treasurer of Ideal China, has a problem The company has just ordered a new kiln for $400,000 Of this sum, $50,000 is described by the supplier as an installation cost Ms Potts does not know whether the Internal Revenue Service (IRS) will permit the company to treat this cost as a tax deductible current expense or as a capital investment In the latter case, the company could depreciate the $50,000 using the five yearMACRStax depreciation schedule Assume the tax rate is 35 and the opportunity cost of capital is 5 Calculate the value of the tax shield if the kiln is currently expensed and if it is treated as a capital investment (Do not round intermediate calculations Round your answers to the nearest whole dollar amount ) Tax shield if currently expensed $ Tax shield if capital investment

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1. Mr. Art Deco will be paid $100,000 one year hence. This is a nominal flow, which he discounts at a nominal discount rate of

Mr. Art Deco will be paid $100,000 one year hence. This is a nominal flow, which he discounts at a nominal discount rate of 8%.

PV = $100,000 / (1 + .08) = $92,593

The inflation rate is 4%.

Calculate the PV of Mr. Decos payment using the equivalentrealcash flow andrealdiscount rate.(You should get exactly the same answer as he did.)

Real cash flow	$
Real discount rate	%
Present value

Machines A and B are mutually exclusive and are expected to produce the following real cash flows:

Cash Flows ($ thousands)
Machine	C₀	C₁	C₂	C₃
A	100	+110	+121
B	120	+110	+121	+133

The real opportunity cost of capital is 10%.

a.Calculate the NPV of each machine

Machine A NPV:

Machine B NPV:

b. Calculate the equivalent annual cash flow from each machine.

Machine A: $

Machine B: $

($ thousands)
Period
	0	1	2	3	4	5	6	7
Net cash flow	12,600	1,484	2,947	6,323	10,534	9,985	5,757	3,269
Present value at 20%	12,600	1,237	2,047	3,659	5,080	4,013	1,928	912
Net present value =	3,802	(sum of PVs)

Restate the above net cash flows in real terms. Discount the restated cash flows at a real discount rate. Assume a 20%nominalrate and 10% expected inflation. NPV should be unchanged at +3,802, or $3,802,000. Fill in the net cash flows for year 0-7 and the NPV at year 0.

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7
Net cash flows (real)
Net present value	$

a result of improvements in product engineering, United Automation is able to sell one of its two milling machines. Both machines perform the same function but differ in age. The newer machine could be sold today for $50,000. Its operating costs are $20,000 a year, but in five years the machine will require a $20,000 overhaul. Thereafter operating costs will be $30,000 until the machine is finally sold in year 10 for $5,000.

The older machine could be sold today for $25,000. If it is kept, it will need an immediate $20,000 overhaul. Thereafter operating costs will be $30,000 a year until the machine is finally sold in year 5 for $5,000.

Both machines are fully depreciated for tax purposes. The company pays tax at 35%. Cash flows have been forecasted in real terms. The real cost of capital is 12%.

a.Calculate the equivalent annual costs for selling the new machine and for selling the old machine.(Do not round intermediate calculations. Enter your answers as a positive value rounded to 2 decimal places.)

	Equivalent Annual Cost
Sell new machine	$
Sell old machine

Low-energy lightbulbs typically cost $3.60, have a life of nine years, and use about $2.00 of electricity a year. Conventional lightbulbs are cheaper to buy, for they cost only $.60. On the other hand, they last only about a year and use about $7.00 of energy.

a.If the real discount rate is 4%, what is the equivalent annual cost of the two products?(Do not round intermediate calculations. Enter your answers as a positive value rounded to 2 decimal places.)

	Equivalent Annual Cost
Low-energy lightbulbs	$
Conventional lightbulbs

The Borstal Company has to choose between two machines that do the same job but have different lives. The two machines have the following costs:

Year	Machine A	Machine B
0	$40,000		$50,000
1	10,000		8,000
2	10,000		8,000
3	10,000	+ replace	8,000
4			8,000	+ replace

These costs are expressed in real terms.

a.Suppose you are Borstals financial manager. If you had to buy one or the other machine and rent it to the production manager for that machines economic life, what annual rental payment would you have to charge?Assume a 6% real discount rate and ignore taxes.(Do not round intermediate calculations.Enter your answers as a positive value rounded to 2 decimal places.)

	Annual Rental Payment
Machine A	$
Machine B

If there is steady 8% per year inflation, what will be the annual rental payment for machine B for the second year?

Year 2 rental payment

Ms. T. Potts, the treasurer of Ideal China, has a problem. The company has just ordered a new kiln for $400,000. Of this sum, $50,000 is described by the supplier as an installation cost. Ms. Potts does not know whether the Internal Revenue Service (IRS) will permit the company to treat this cost as a tax-deductible current expense or as a capital investment. In the latter case, the company could depreciate the $50,000 using the five-yearMACRStax depreciation schedule.

Assume the tax rate is 35% and the opportunity cost of capital is 5%. Calculate the value of the tax shield if the kiln is currently expensed and if it is treated as a capital investment.(Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)