Question

(NPV with varying required rates of return​) Gubanich Sportswear is considering building a new factory to produce aluminum baseball bats. This project would require an initial cash outlay of ​$5,000,000 and would generate annual free cash inflows of ​$1,100,000 per year for 8 years. Calculate the​ project's NPV ​given:

a. A required rate of return of 7 percent

b. A required rate of return of 11 percent

c. A required rate of return of 13 percent

d. A required rate of return of 18 percent

Answer 1

When cash flows are even each year, annuity factor can be used

Net Present Value

= Present value of inflows – Initial Investment

Present Value of inflows

= Annual cash inflow x Annuity Factor

Annuity Factor

= [ 1 – (1 + r) ^ - n ] / r

Where,

r = Required rate of return

n = Number of years

Annuity factors for r = 7, 11, 13 and 18 are calculated below :

r = 7

Annuity Factor

= [ 1 – (1.07 ^ - 8)] / 0.07

= [ 1 - 0.582009] / 0.07

= 5.971298

Similarly, for r = 11

Annuity Factor

= [ 1 – ( 1.11 ^ -8)] / 0.11

= [ 1 - 0.433926] / 0.11

= 5.146123

Similarly, for r = 13

Annuity Factor

= [ 1 – ( 1.13 ^ -8)] / 0.13

= [ 1 - 0.376160] / 0.13

= 4.798770

And For r = 18

Annuity Factor

= [ 1 – ( 1.18 ^ -8)] / 0.18

= [ 1 - 0.266038] / 0.18

= 4.07757

a)

So, NPV

= $ 1,100,000 x 5.971298 - $5,000,000

= $6,568,428.35 - $5,000,000

= $1,568,428.36

b)

NPV

= $ 1,100,000 x 5.146123 - $5,000,000

= $5,660,735.04 - $5,000,000

= $660,735.04

c)

NPV

= $ 1,100,000 x 4.798770 - $5,000,000

= $5,278,647.32 - $5,000,000

= $278,647.32

d)

NPV

= $ 1,100,000 x 4.07757 - $5,000,000

= $4,485,323.33 - $5,000,000

=- $514,676.66

Answer 2

SOLUTION :

Gubanich sportswear : 

a.

Initial cost = 5000000 ($)

Discount rate , r = 7% = 0.07

=> (1 + r) = 1.09

Project generates $1100000 per year for 8 years.

So,

NPV 

= - Initial cost + PV of future cash flows

= - 5000000 + 1100000(1.07^8 - 1)/(0.07*1.07^8)

= 1568428.36 ($) 

If the discount rate is 9%, then the project’s NPV = 1568428.36 ($) 

(ANSWER).

b.

Initial cost = 5000000 ($)

Discount rate , r = 11% = 0.11

=> (1 + r) = 1.11

Project generates $1100000 per year for 8 years.

So,

NPV 

= - Initial cost + PV of future cash flows

= - 5000000 + 1100000(1.11^8 - 1)/(0.11*1.11^8)

= 660735.04 ($) 

If the discount rate is 9%, then the project’s NPV = 660735,04 ($) 

(ANSWER).

c.

Initial cost = 5000000 ($)

Discount rate , r = 13% = 0.13

=> (1 + r) = 1.13

Project generates $1100000 per year for 8 years.

So,

NPV 

= - Initial cost + PV of future cash flows

= - 5000000 + 1100000(1.13^8 - 1)/(0.13*1.13^8)

= 278647.32 ($) 

If the discount rate is 9%, then the project’s NPV = 278647.32 ($) 

(ANSWER).

d.

Initial cost = 5000000 ($)

Discount rate , r = 18% = 0.18

=> (1 + r) = 1.18

Project generates $1100000 per year for 8 years.

So,

NPV 

= - Initial cost + PV of future cash flows

= - 5000000 + 1100000(1.18^8 - 1)/(0.18*1.18^8)

= - 514677.67 ($) 

If the discount rate is 9%, then the project’s NPV = - 514677.67 ($) 

(ANSWER).