discount rate is 14 Service Fusion ccess Connect ervice Fusi

discount rate is 14%

Service Fusion ccess Connect ervice Fusion nnect.mheducation.com/flow/connect.html haseImported From Firefc r 7-Net Present Value and Oth.. Saved ent project has annual cash inflows of $4,400. $3,900, $5.100, and $4.300, and a discount rate discounted payback period for these cash flows if the initial cost is $5.700? (Do not round inte r answer to 2 decimal places, e.g., 32.16.) d payback period years r enswer to 2 decimal places, e.g., 32.16.) d payback periodyears e discounted payback period for these cash flows if the initial cost is $10.800? (Do not ro ayback period for these cash flows if the initial cost is $7800? (Do not round inte und int ur answer to 2 decimal places, e.g., 32.16.) ed payback periodyears

Solution

Workings:

Cash flow is provided for 4 years annually.

Discounted Cash flow of year 1 at year 0 = 4,400 * (1 + 0.14)^(-1) = 3,859.649

Discounted Cash flow of year 2 at year 0 = 3,900 * (1 + 0.14)^(-2) = 3,000.923

Discounted Cash flow of year 3 at year 0 = 5,100 * (1 + 0.14)^(-3) = 3,442.354

Discounted Cash flow of year 4 at year 0 = 4,300 * (1 + 0.14)^(-4) = 2,545.945

Cumulative DCF at year 1 = DCF at year 1 = 3,859.649

Cumulative DCF at year 2 = DCF at year 1 + year 2 = 3,859.649 + 3,000.923 = 6,860.572

Cumulative DCF at year 3 = DCF at year 1 + year 2 + year3 = 3,859.649 + 3,000.923 + 3,442.354 = 10,302.927

Cumulative DCF at year 4 = DCF at year 1 + year 2 + year3 + year 4 = 3,859.649 + 3,000.923 + 3,442.354 + 2,545.945 = 12,848.872

1. Discounted payback period (DPP) when initial cost is 5,700 and discount rate is 14%:

Cumulative DCF at year 1 is 3,859.649 which is lower than initial cost of 5,700, so DPP will be greater than 1.

DPP = 1 + (5,700 - 3,859.649) / (6,860.57 - 3,859.649) = 1.61 years

2. Discounted payback period (DPP) when initial cost is 7,800 and discount rate is 14%:

Cumulative DCF at year 2 is 6,860.57 which is lower than initial cost of 7,800. So, DPP will be greater than 2.

DPP = 2 + (7,800 - 6,860.572) / (10,302.927 - 6,860.572) = 2.27 years

3. Discounted payback period (DPP) when initial cost is 10,800 and discount rate is 14%:

Cumulative DCF at year 3 is 10,302.927 which is lower than initial cost of 10,800. So, DPP will be greater than 3.

DPP = 3 + (10,800 - 10,302.927) / (12,848.872 - 10,302.927) = 3.195 years = 3.20 years

Year	Cash flow	Discounted Cash flow at year 0 (DCF)	Cumulative DCF
1	4,400.00	3,859.64912	3,859.64912
2	3,900.00	3,000.92336	6,860.57248
3	5,100.00	3,442.35473	10,302.92722
4	4,300.00	2,545.94519	12,848.87241