Question

2

Brett Collins is reviewing his company's investment in a cement plant. The company paid $15,400,000 five years ago to acquire the
plant. Now top management is considering an opportunity to sell it. The president wants to know whether the plant has met original
expectations before he decides its fate. The company's desired rate of return for present value computations is 10 percent. Expected
and actual cash flows follow: (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.)
37:23
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Expected
Actual
Year 1
$3,320,000
2,690,000
Year 2
$5,000,000
2,970,000
Net present value (expected)
Net present value (actual)
Year 3
$4,610,000
4,850,000
Year 4
$5,140,000
3,820,000
Required
a.&b. Compute the net present value of the expected and actual cash flows as of the beginning of the investment. (Negative amounts
should be indicated by a minus sign. Round your intermediate calculations and final answer to the nearest whole dollar.)
Year 5
$4,230,000
3,530,000
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Answer 1

Step-by-step explanation:

To compute the net present value (NPV) of the expected and actual cash flows, we need to find the present value of each cash flow and then subtract the initial investment.

Given:

Initial Investment (Year 0) = $15,400,000

Desired Rate of Return = 10% or 0.10

a. Net Present Value (Expected Cash Flows):

Year 1 Cash Flow = $3,320,000

Year 2 Cash Flow = $5,000,000

Year 3 Cash Flow = $4,610,000

Year 4 Cash Flow = $5,140,000

Year 5 Cash Flow = $4,230,000

PV Factor (10%, n = 1) = 1 / (1 + 0.10)^1 = 0.9091

PV Factor (10%, n = 2) = 1 / (1 + 0.10)^2 = 0.8264

PV Factor (10%, n = 3) = 1 / (1 + 0.10)^3 = 0.7513

PV Factor (10%, n = 4) = 1 / (1 + 0.10)^4 = 0.6830

PV Factor (10%, n = 5) = 1 / (1 + 0.10)^5 = 0.6209

Net Present Value (Expected) =

[(Year 1 Cash Flow * PV Factor (10%, n = 1)) +

(Year 2 Cash Flow * PV Factor (10%, n = 2)) +

(Year 3 Cash Flow * PV Factor (10%, n = 3)) +

(Year 4 Cash Flow * PV Factor (10%, n = 4)) +

(Year 5 Cash Flow * PV Factor (10%, n = 5))] - Initial Investment

Net Present Value (Expected) =

[(3,320,000 * 0.9091) + (5,000,000 * 0.8264) + (4,610,000 * 0.7513) + (5,140,000 * 0.6830) + (4,230,000 * 0.6209)] - 15,400,000

Net Present Value (Expected) ≈ [3,023,912 + 4,132,000 + 3,457,093 + 3,512,620 + 2,626,470] - 15,400,000

Net Present Value (Expected) ≈ 16,751,095 - 15,400,000

Net Present Value (Expected) ≈ $1,351,095

b. Net Present Value (Actual Cash Flows):

Year 1 Cash Flow (Actual) = $2,690,000

Year 2 Cash Flow (Actual) = $2,970,000

Year 3 Cash Flow (Actual) = $4,850,000

Year 4 Cash Flow (Actual) = $3,820,000

Year 5 Cash Flow (Actual) = $3,530,000

Net Present Value (Actual) =

[(Year 1 Cash Flow * PV Factor (10%, n = 1)) +

(Year 2 Cash Flow * PV Factor (10%, n = 2)) +

(Year 3 Cash Flow * PV Factor (10%, n = 3)) +

(Year 4 Cash Flow * PV Factor (10%, n = 4)) +

(Year 5 Cash Flow * PV Factor (10%, n = 5))] - Initial Investment

Net Present Value (Actual) =

[(2,690,000 * 0.9091) + (2,970,000 * 0.8264) + (4,850,000 * 0.7513) + (3,820,000 * 0.6830) + (3,530,000 * 0.6209)] - 15,400,000

Net Present Value (Actual) ≈ [2,447,890 + 2,454,888 + 3,645,805 + 2,607,860 + 2,197,917] - 15,400,000

Net Present Value (Actual) ≈ 13,354,360 - 15,400,000

Net Present Value (Actual) ≈ -$2,045,640

So, the Net Present Value of the expected cash flows is approximately $1,351,095, while the Net Present Value of the actual cash flows is approximately -$2,045,640.