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​(NPV with varying required rates of return​) Gubanich Sportswear is considering building a new factory to...

​(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 4,000,000 and would generate annual free cash inflows of 1,200,000 per year for 7 years. Calculate the​ project's NPV ​given:

a. A required rate of return of 9 percent

b. A required rate of return of 11 percent

c. A required rate of return of 15 percent

d. A required rate of return of 17 percent

Solutions

Expert Solution

Net Present value (NPV) is the present value of future cash inflows minus the initial investment

Here, since the cash flows are equal every year, so it is an annuity. We have to find present value of the annuity of $1200000 after 7 years. We will use the present value of annuity table to find the required NPV.

(a) At rate of 9%

Present value of future cash flows = $1200000 * PVA (9%, 7 Years)

where, PVA (9%, 7 years) is the present value of $1 annuity at 9% for 7 years. ( since the annual payments are of equal amount of $1200000, so it will be an annuity and we will use the present value of annuity table).

From the table the value of PVA (9%, 7 Years) is 5.0330

Putting this value in the above equation, we get,

Present value of future cash flows = $1200000 * 5.0330 = $6039600

Initial investment (given) = $4000000

Net Present value (NPV) = Present value of future cash inflows - initial investment

Net Present value (NPV) = $6039600 - $4000000 = $2039600

(b) At rate of 11%

Present value of future cash flows = $1200000 * PVA (11%, 7 Years)

where, PVA (11%, 7 years) is the present value of $1 annuity at 11% for 7 years. ( since the annual payments are of equal amount of $1200000, so it will be an annuity and we will use the present value of annuity table).

From the table the value of PVA (11%, 7 Years) is 4.7122

Putting this value in the above equation, we get,

Present value of future cash flows = $1200000 * 4.7122 = $5654640

Initial investment (given) = $4000000

Net Present value (NPV) = Present value of future cash inflows - initial investment

Net Present value (NPV) = $5654640 - $4000000 = $1654640

(c) At rate of 15%

Present value of future cash flows = $1200000 * PVA (15%, 7 Years)

where, PVA (15%, 7 years) is the present value of $1 annuity at 15% for 7 years. ( since the annual payments are of equal amount of $1200000, so it will be an annuity and we will use the present value of annuity table).

From the table the value of PVA (15%, 7 Years) is 4.1604

Putting this value in the above equation, we get,

Present value of future cash flows = $1200000 * 4.1604 = $4992480

Initial investment (given) = $4000000

Net Present value (NPV) = Present value of future cash inflows - initial investment

Net Present value (NPV) = $4992480 - $4000000 = $992480

(d) At rate of 17%

Present value of future cash flows = $1200000 * PVA (17%, 7 Years)

where, PVA (17%, 7 years) is the present value of $1 annuity at 17% for 7 years. ( since the annual payments are of equal amount of $1200000, so it will be an annuity and we will use the present value of annuity table).

From the table the value of PVA (17%, 7 Years) is 3.92

Putting this value in the above equation, we get,

Present value of future cash flows = $1200000 * 3.92 = $4704000

Initial investment (given) = $4000000

Net Present value (NPV) = Present value of future cash inflows - initial investment

Net Present value (NPV) = $4704000 - $4000000 = $704000

jeff jeffy answered 1 year ago
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