Question

You are a manager at a manufacturing company. Today (year 0), you are considering buying a new product line that produces ventilators. Here are the details of this project:

• At year 0, you will purchase the manufacturing equipment needed for $5,000,000. The equipment can be depreciated to zero using straight line depreciation over five years (year 1-5). At the end of year 5, the book value of the equipment becomes $0, and you will sell it for $500,000.

• You anticipate selling 1,024 ventilators in year 1 and year 2. Starting from year 3, the number of ventilators you sell will decrease by 25% every year through the fifth year of sales year 5. After year 5, the product will be obsolete and sales will be 0 beginning in year 6.

• Each ventilator sells for $25,000 in year 1. The sales price will increase by 5% each subsequent year.

• The cost making each ventilator is $20,000 in year 1, but the cost per unit will increase by 5% each subsequent year. • From year 1 to 5, you also incur some general and administrative expenses that are 5% of the annual total sales.

• You offer your alumni the opportunity to pay for their ventilators one year after purchase. You anticipate that 10% of your customers are alumni and will take advantage of this offer. • 20% of next-year’s costs of goods sold will be held as inventory.

• Your tax rate is 40%.

• The appropriate nominal (after-tax) discount rate for this project is 15%.

Assume all cash flows are nominal. Expand your cell to show 4 decimal places (e.g., $12.4567). What is the net present value of this project?

Answer 1

	T0	T1	T2	T3	T4	T5	Calculation
Investment	-5000000.0000
Sales units		1024.0000	1024.0000	768.0000	576.0000	432.0000	T1& T2 given. T3-T5 - 75% of previous year
Sale price per unit		25000.0000	26250.0000	27562.5000	28940.6250	30387.6563	Sales prices increase by 5% T2-T5
Cost per unit		-20000.0000	-21000.0000	-22050.0000	-23152.5000	-24310.1250	cost prices increase by 5% T2-T5
sales value		25600000.0000	26880000.0000	21168000.0000	16669800.0000	13127467.5000	Units * sales price per unit
Cost value		-20480000.0000	-21504000.0000	-16934400.0000	-13335840.0000	-10501974.0000	Units * cost per unit
General and admin expense		-1280000.0000	-1344000.0000	-1058400.0000	-833490.0000	-656373.3750	5% of sales value
Deprecaition		-1000000.0000	-1000000.0000	-1000000.0000	-1000000.0000	-1000000.0000	Investment / 5
Profit on sale of machine						500000.0000	Salvage value - Bookvalue. Bookvalue is 0 at year 5
Profit before tax		2840000.0000	3032000.0000	2175200.0000	1500470.0000	1469120.1250	Sales - cost - General admin expense- Depreciation
Tax		-1136000.0000	-1212800.0000	-870080.0000	-600188.0000	-587648.0500	Profit before tax * 40%
Profit after tax		1704000.0000	1819200.0000	1305120.0000	900282.0000	881472.0750	Profit before tax - tax
Add non cash items
Depreciation		1000000.0000	1000000.0000	1000000.0000	1000000.0000	1000000.0000	Depreciation as above
Cash flow from operations		2704000.0000	2819200.0000	2305120.0000	1900282.0000	1881472.0750	Profit after tac + Depreciation
Working capital
Receivables		-2560000.0000	-128000.0000	571200.0000	449820.0000	1666980.0000	10% of sales value - previous year receivables. See note
Inventory		-4096000.0000	-204800.0000	913920.0000	719712.0000	2667168.0000	20% of cost- previous year inventory. See note
Total working capital		-6656000.0000	-332800.0000	1485120.0000	1169532.0000	4334148.0000
Total cashflow	-5000000.0000	-3952000.0000	2486400.0000	3790240.0000	3069814.0000	6215620.0750	Cash flow from operations + Total working capital
Discount factor @ 15%	1.0000	0.8696	0.7561	0.6575	0.5718	0.4972	=(1/1.15^n)
NPV	-5000000.0000	-3436521.7391	1880075.6144	2492144.3248	1755176.1179	3090261.6967
Total NPV	781136.0147
Notes
Receivables are debtors amount collected at 1 year lag. So T1 is 10% of T1 sales. This amount will be received on T2 and only excess sales will have 10% receivables. Ie. 10% of T2 sales - T1 receviables. T3 as sales value reduce, the receivables working capital starts to generate cash inflows. T3 = 10% of sales - T2 - T1 receivables. . T5 is just receiving entire cost which was not recovered in T4 and T3. So T1 - T5 will be 0
Inventories are excess inventory over sales kept for business. This requires investment of working capital. So T1 is 20% of T1 cost of sales. This amount will be reasiled on T2 and only excess inventory will require 20% investment. Ie. 20% of T2 cost of sales - T1 receviables. T3 as sales value reduce, the inventory working capital starts to generate cash inflows. T3 = 10% of sales - T2 - T1 inventories. T5 is just receiving entire cost which was not recovered in T4 and T3. So T1 - T5 will be 0