Question

Let's say we are planning on adding a very large modern sign to attract customers to our marijuana and tattoo shop that we run just north of Denver. We've completed a ton of market analysis and we are fairly confident that the sign will increase sales by $50,000 per year for the first two years, and then we think it will result in an increase of $35,000 per year for the next four years. The margins we earn on our sales of marijuana is 70% and the margins we earn on our tattoos is 40%. We expect that the incremental sales resulting from the sign will be split 50-50 between marijuana products and tattoo services.

The sign will cost us $110, 000 and the company has no debt. The owners of the company expect to earn 15% on the funds they invest in the company. After six years, the sign will likely be taken down and sold for scrap to yield $5,000.

Calculate the net present value. Ignore taxes.

Answer 1

Initial Investment required for modern sign = $110,000 ----- (1)

Owners expected rate of return(Discount Rate) = 15%

Increase in sales per year for first two years = $50,000

Increase in sales per year from year 3 to year 6 =$35,000

Margin on Marijuana = 70% (of sales)

Margin on Tattoos = 40% (of sales)

Sales split between Marijuana and Tattoo services = 50:50(1:1)(equal)

Total Margin across different years (Total Margin = Margin from Marijuana + Margin from Tattoo Services)

Years	1	2	3	4	5	6
Total extra sales because of sign	$         50,000	$         1,00,000	$         1,35,000	$         1,70,000	$         2,05,000	$         35,000
Margin from Marijuana sales	$         17,500	$            35,000	$            47,250	$            59,500	$            71,750	$         84,000
Margin from Tattoo Services	$         10,000	$            20,000	$            27,000	$            34,000	$            41,000	$         48,000
Total Margin	$         27,500	$            55,000	$            74,250	$            93,500	$         1,12,750	$     1,32,000

Present Value of total margin(cash flow) from any year X = (Total Margin in year x)/.(1+discount rate)^x

Present Value of cash flow from year 1 = ($27,500)/(1+15%)

Similar to above, Present Value of (total margin) cash flows across different years

Years	1	2	3	4	5	6
Present Value of Total Margin	$         23,913	$            41,588	$            48,821	$            53,459	$            56,057	$         57,067

Sum of Present Value of Total Margins across different years = $2,80,904.37 ---- (2)

Salvage Value at the end of 6 years = $5,000

Present Value of Salvage value = $5,000/(1.15)^6 = $2161.64 ---- (3)

Net Present Value (NPV) = Sum of Present Value of Total Margins across different years + Present Value of Salvage value - Initial Investment

= $2,80,904.37 + $2161.64 - $110,000 = $1,75,252.2 (From 1,2 and 3)

Net Present Value(NPV) = $1,73,066.01