Whay is the payback period of the following investment when

Whay is the payback period of the following investment when a) i=0% and b) i=10%/ year?

Initial Cost ($) 1,000,000

Annual Cost ($) 100,000

Annual income ($) 300,000

salvage Value ($) 500,000

Max Life time: 10 years

Solution

PAYBACK PERIOD CALCULATION (No interest) Year Investment Salvage value Annual income Annual Cost Interest Net Income Value 0 $10,00,000 $5,00,000 $5,00,000 1 $3,00,000 $1,00,000 $0 $2,00,000 $3,00,000 2 $3,00,000 $1,00,000 $0 $2,00,000 $1,00,000 3 $3,00,000 $1,00,000 $0 $2,00,000 -$1,00,000 4 $3,00,000 $1,00,000 $0 $2,00,000 -$3,00,000 5 6 Payback is between 2 and 3 years (2.5 years) 7 8 9 10 PAYBACK PERIOD CALCULATION (With interest) 10.00% Year Investment Salvage value Annual income Annual Cost Interest Net Income Value 0 $10,00,000 $5,00,000 $10,00,000 1 $3,00,000 $1,00,000 $1,00,000 $1,00,000 $9,00,000 2 $3,00,000 $1,00,000 $90,000 $1,10,000 $7,90,000 3 $3,00,000 $1,00,000 $79,000 $1,21,000 $6,69,000 4 $3,00,000 $1,00,000 $66,900 $1,33,100 $5,35,900 5 $3,00,000 $1,00,000 $53,590 $1,46,410 $3,89,490 Payback is between 4 and 5 years as after 4 years the value is close to its salvage value