A company is introducing a new product that they think will

) A company is introducing a new product that they think will have a 10-year life cycle,
with sales increasing steadily for 5 years, after which sales will decline steadily. The
company feels that the product will be so successful that they will make sales every day
of the year. As a result, they model future sales by assuming net cash flows are received
continuously over the 10-year horizon at the following rates;
100t, for 0?t?5
100(10-t), for 5<t?10.
The company requires an effective annual rate of return on any investment of 12.7.
What is the maximum amount of money the company should spend today to invest in
this new product?) A company is introducing a new product that they think will have a 10-year life cycle,
with sales increasing steadily for 5 years, after which sales will decline steadily. The
company feels that the product will be so successful that they will make sales every day
of the year. As a result, they model future sales by assuming net cash flows are received
continuously over the 10-year horizon at the following rates;
100t, for 0?t?5
100(10-t), for 5<t?10.
The company requires an effective annual rate of return on any investment of 12.7.
What is the maximum amount of money the company should spend today to invest in
this new product?) A company is introducing a new product that they think will have a 10-year life cycle,
with sales increasing steadily for 5 years, after which sales will decline steadily. The
company feels that the product will be so successful that they will make sales every day
of the year. As a result, they model future sales by assuming net cash flows are received
continuously over the 10-year horizon at the following rates;
100t, for 0?t?5
100(10-t), for 5<t?10.
The company requires an effective annual rate of return on any investment of 12.7.
What is the maximum amount of money the company should spend today to invest in
this new product?

Solution

For the first 5 years, we use the formula 100t where t =0 to 5

Cash flow in year 0 = 100 *0 =0

Cash flow for year 1 = 100*1 = 100

Cash flow for year 2,3,4,5 = 200,300,400 and 500

Cash flow = 100*(10-t) for t = 6 to 10

Cash flow in year 6 = 100*(10-6) = 100*4 = 400

Cash flow in year 7 = 100*(10-7) =100*3 =300

Similarly cash flow in year 8,9 and 10 = 200,100,0

Present value of these futrure cash flows at 12.7% is calculated as follows:

PV = 0 +100/1.127 +200/1.127^2 + 300/1.127^3 +400/1.127^4 +500/1.127^5 +400/1.127^6 +300/1.127^7 +200/1.127^8 +100/1.127^9 +0 = 1,414.81

The maximum amount of money the company should spend today to invest in this new product =$1,414.81