Net Present Value and Cash Flow
8. Year 0 Year 1 Year 2
Taxable income $9,100 $10,250 $15,300
Marginal tax rate .30 .30 .30
Tax $2,730 $3,075 $4,590
Revenue $13,000 $16,250 $23,400
Expenses (4,250) (8,000) (8,100)
Tax cost (2,730) (3,075) (4,590)
Net cash flow $6,020 $5,175 $10,710
Discount factor (6%) .943 .890
Present value $6,020 $4,880 $9,532
NPV $20,432
11. a. Year 0 Year 1 Year 2 Year 3 Year 4
Before-tax cash flow $(500,000) $52,500 $47,500 $35,500 $530,500
Tax cost (7,875) (7,125) (5,325) (4,575) After-tax cash flow 44,625 40,375 30,175 525,925
Discount factor (7%) .935 .873 .816 .763
Present value $(500,000) $41,724 $35,247 $24,623 $401,281
NPV $2,875
Investor W should make the investment because NPV is positive.
b. Year 0 Year 1 Year 2 Year 3 Year 4
Before-tax cash flow $(500,000) $52,500 $47,500 $35,500 $530,500
Tax cost (10,500) (9,500) (7,100) (6,100) After-tax cash flow 42,000 38,000 28,400 524,400
Discount factor (7%) .935 .873 .816 .763
Present value $(500,000) $39,270 $33,174 $23,174 $400,117
NPV $(4,265)
Investor W should not make the investment because NPV is negative.
c. Year 0 Year 1 Year 2 Year 3 Year 4
Before-tax cash flow $(500,000) $52,500 $47,500 $35,500 $530,500
Tax cost (5,250) (4,750) (8,875) (7,625) After-tax cash flow 47,250 42,750 26,625 522,875
Discount factor (7%) .935 .873 .816 .763
Present value $(500,000) $44,179 $37,321 $21,726 $398,954
NPV $2,180
Investor W should make the investment because NPV is positive.
16. a. Opportunity 1: Year 0 Year 1 Year 2
Taxable income (loss) $(8,000) $5,000 $20,000
Marginal tax rate .40 .40 .40
Tax $(3,200) $2,000 $8,000
Before-tax cash flow $(8,000) $5,000 $20,000
Tax (cost) or savings 3,200(2,000) (8,000)
Net cash flow $(4,800) $3,000 $12,000
Discount factor (12%) .893 .797
Present value $(4,800) $2,679 $9,564
NPV $7,443
Opportunity 2: Year 0 Year 1 Year 2
Taxable income $5,000 $5,000 $5,000
Marginal tax rate .40 .40 .40
Tax $2,000
Taxable income $9,100 $10,250 $15,300
Marginal tax rate .30 .30 .30
Tax $2,730 $3,075 $4,590
Revenue $13,000 $16,250 $23,400
Expenses (4,250) (8,000) (8,100)
Tax cost (2,730) (3,075) (4,590)
Net cash flow $6,020 $5,175 $10,710
Discount factor (6%) .943 .890
Present value $6,020 $4,880 $9,532
NPV $20,432
11. a. Year 0 Year 1 Year 2 Year 3 Year 4
Before-tax cash flow $(500,000) $52,500 $47,500 $35,500 $530,500
Tax cost (7,875) (7,125) (5,325) (4,575) After-tax cash flow 44,625 40,375 30,175 525,925
Discount factor (7%) .935 .873 .816 .763
Present value $(500,000) $41,724 $35,247 $24,623 $401,281
NPV $2,875
Investor W should make the investment because NPV is positive.
b. Year 0 Year 1 Year 2 Year 3 Year 4
Before-tax cash flow $(500,000) $52,500 $47,500 $35,500 $530,500
Tax cost (10,500) (9,500) (7,100) (6,100) After-tax cash flow 42,000 38,000 28,400 524,400
Discount factor (7%) .935 .873 .816 .763
Present value $(500,000) $39,270 $33,174 $23,174 $400,117
NPV $(4,265)
Investor W should not make the investment because NPV is negative.
c. Year 0 Year 1 Year 2 Year 3 Year 4
Before-tax cash flow $(500,000) $52,500 $47,500 $35,500 $530,500
Tax cost (5,250) (4,750) (8,875) (7,625) After-tax cash flow 47,250 42,750 26,625 522,875
Discount factor (7%) .935 .873 .816 .763
Present value $(500,000) $44,179 $37,321 $21,726 $398,954
NPV $2,180
Investor W should make the investment because NPV is positive.
16. a. Opportunity 1: Year 0 Year 1 Year 2
Taxable income (loss) $(8,000) $5,000 $20,000
Marginal tax rate .40 .40 .40
Tax $(3,200) $2,000 $8,000
Before-tax cash flow $(8,000) $5,000 $20,000
Tax (cost) or savings 3,200(2,000) (8,000)
Net cash flow $(4,800) $3,000 $12,000
Discount factor (12%) .893 .797
Present value $(4,800) $2,679 $9,564
NPV $7,443
Opportunity 2: Year 0 Year 1 Year 2
Taxable income $5,000 $5,000 $5,000
Marginal tax rate .40 .40 .40
Tax $2,000