Question

McCann Co. has identified an investment project with the following cash flows. Year Cash Flow 1 $ 530 2 690 3 875 4 1,090 a. If the discount rate is 10 percent, what is the present value of these cash flows? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the present value at 18 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What is the present value at 24 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The present value of cash flows is calculated for three different discount rates. At 10%, 18%, and 24%, the totals are $2,457.92, $2,015.18, and $1,786.59 respectively. These calculations show the impact of the discount rate on the present value of future cash flows.

Step-by-step explanation:

Calculating the present value (PV) of future cash flows is a fundamental concept in finance that allows us to determine the value of cash flows at a given discount rate. PV calculations are important in various financial contexts, including valuing investments, bonds, and annuities.

Part a - Present Value at 10%

Year 1: $530 / (1 + 0.10)¹ = $481.82
Year 2: $690 / (1 + 0.10)² = $567.90
Year 3: $875 / (1 + 0.10)³ = $656.76
Year 4: $1,090 / (1 + 0.10)⁴ = $751.44
Total PV at 10%: $481.82 + $567.90 + $656.76 + $751.44 = $2,457.92

Part b - Present Value at 18%

Year 1: $530 / (1 + 0.18)¹ = $449.15
Year 2: $690 / (1 + 0.18)² = $495.29
Year 3: $875 / (1 + 0.18)³ = $525.94
Year 4: $1,090 / (1 + 0.18)⁴ = $544.80
Total PV at 18%: $449.15 + $495.29 + $525.94 + $544.80 = $2,015.18

Part c - Present Value at 24%

Year 1: $530 / (1 + 0.24)¹ = $427.42
Year 2: $690 / (1 + 0.24)² = $446.76
Year 3: $875 / (1 + 0.24)³ = $455.44
Year 4: $1,090 / (1 + 0.24)⁴ = $456.97
Total PV at 24%: $427.42 + $446.76 + $455.44 + $456.97 = $1,786.59

Answer 2

A. $2,453.95

B. $2,039.46

C. $1,796.14

Step-by-step explanation:

The computation of the Present value is shown below

= Present value of all yearly cash inflows after applying discount factor

The discount factor should be computed by

= 1 ÷ (1 + rate) ^ years

where,

(A) Rate is 10%

Year = 0,1,2,3,4

Discount Factor:

For Year 1 = 1 ÷ 1.1 ^1 = 0.9091

For Year 2 = 1 ÷ 1.1 ^2 = 0.8264

For Year 3 = 1 ÷ 1.1 ^3 = 0.7513

For Year 4 = 1 ÷ 1.1 ^4 = 0.6830

So, the calculation of a Present value of all yearly cash inflows are shown below

= Year 1 cash inflow × Present Factor of Year 1 + Year 2 cash inflow × Present Factor of Year 2 + Year 3 cash inflow × Present Factor of Year 3 + Year 4 cash inflow × Present Factor of Year 4

= $530 × 0.9091 + $690 × 0.8264 + $875 × 0.7513 + $1,090 × 0.6830

= $481.82 + $570.25 + $657.40 + $744.48

= $2,453.95

(B) Rate is 18%

Year = 0,1,2,3,4

Discount Factor:

For Year 1 = 1 ÷ 1.18 ^ 1 = 0.8475

For Year 2 = 1 ÷ 1.18 ^2 = 0.7182

For Year 3 = 1 ÷ 1.18 ^3 = 0.6086

For Year 4 = 1 ÷ 1.18 ^4 = 0.5158

So, the calculation of a Present value of all yearly cash inflows are shown below

= Year 1 cash inflow × Present Factor of Year 1 + Year 2 cash inflow × Present Factor of Year 2 + Year 3 cash inflow × Present Factor of Year 3 + Year 4 cash inflow × Present Factor of Year 4

= $530 × 0.8475 + $690 × 0.7182 + $875 × 0.6086 + $1,090 × 0.5158

= $449.15 + $495.55 + $532.55 + $562.21

= $2,039.46

(C) Rate is 24%

Year = 0,1,2,3,4

Discount Factor:

For Year 1 = 1 ÷ 1.24 ^ 1 = 0.8065

For Year 2 = 1 ÷ 1.24 ^2 = 0.6504

For Year 3 = 1 ÷ 1.24 ^3 = 0.5245

For Year 4 = 1 ÷ 1.24 ^4 = 0.4230

So, the calculation of a Present value of all yearly cash inflows are shown below

= Year 1 cash inflow × Present Factor of Year 1 + Year 2 cash inflow × Present Factor of Year 2 + Year 3 cash inflow × Present Factor of Year 3 + Year 4 cash inflow × Present Factor of Year 4

= $530 × 0.8065 + $690 × 0.6504 + $875 × 0.5245 + $1,090 × 0.4230

= $427.42 + $448.75 + $458.93 + $461.04

= $1,796.14