Please answer the following finance questions. PLEASE SHOW AND EXPLAIN ALL WORK!
ID: 2661264 • Letter: P
Question
Please answer the following finance questions. PLEASE SHOW AND EXPLAIN ALL WORK!
1. Graham Inc. plans to buy a new machine, which costs $120,000. Graham will depreciate it fully over its useful life of 6 years, on a straight-line basis. It will then sell the machine for $20,000. Graham has an income tax rate of 32% and it uses a discount rate of 10%. Calculate the minimum pre-tax annual earnings generated by this machine to justify its purchase.
2. Munger Company plans to buy a machine for $180,000 with uncertain life. The resale value of the machine is zero. The following table shows its expected life :
Expected Life______Probability
5 years____________25%
6 years____________30%
7 years____________45%
The machine will save the company $50,000 annually while its running. Munger will depreciate it fully on a straight-line basis in 6 years. The tax rate of Munger is 32%, and the proper discount rate in this case is 12%. Should Munger buy this machine?
3. The H. Marks Company plans to buy a new machine for $70,000, which will save the company $17,000 annually. H. Marks will depreciate the machine on the ACRS with three-year life, the annual depreciation being 24%, 48%, and 28%. The company will use the equipment for 5 years, and then sell it for $12,000. The tax rate of the company is 31% and it will use 11% as the discount rate. Should H. Marks buy this machine?
4. T. Gayner Corp. plans to buy a machine and depreciate it fully over the next five years. The following table shows the expected life of the machine :
Probability________Expected Life
20%______________6 years
30%______________7 years
50%______________8 years
The machine will generate pre-tax savings of $20,000 annually. The tax rate of T. Gayner is 33%, and the proper discount rate is 12%. What is the maximum price that T. Gayner should pay for the machine?
Explanation / Answer
1).
depreciation per year = 120000/6 = 20000
let pre tax anuual earning be x
profit after tax = .68x
cash flow for year 1 to 5 = .68x+20000
cash flow for year 6 = .68x+40000
its npv should be equal to 120000
120000= .68x+20000)*PVIFA(10,6)+20000/1.1^6
120000 = .68X+20000)*4.3553+11289.47
.68X+20000 = 120000-11289.47)/4.3553 = 24960.51
x = 4960.51/.68 = $7294.86
2).
let expected life be 5 year
depreciation per year = 180000/6 = 30000
profit per year = (50000-30000)*(1-.32) = $13600
cash flow per year = 13600+30000 = $43600
PV = 43600*PVIFA(12,5) = 43600*3.6048 = $157169.28
now, let expected lyf be 6 year
depreciation per year = 180000/6 = 30000
profit per year = (50000-30000)*(1-.32) = $13600
cash flow per year = 13600+30000 = $43600
PV = 43600*PVIFA(12,6) = 43600*4.1114 = $179257.04
let expected lyf be 7 year
depreciation per year = 180000/6 = 30000
profit per year = (50000-30000)*(1-.32) = $13600
cash flow per year till year 6 = 13600+30000 = $43600
cash flow for year 7, = 50000*(1-.32) = $34000
PV = 43600*PVIFA(12,6)+(34000/1.12^7) = 43600*4.1114+(34000/1.12^7) = $194636.91
expected over all PV = .25*157169.28+.30*179257.04+.45*194636.91 = $180656.04
its initial cost = 180000
expected PV = $180656.04 > intial cost
so, he should buy the machine
depreciation for year 1 = .24*70000 = 16800
depreciation for year 2 = .48*70000 = 33600
depreciaitob for yr 3 = .28*70000 = 19600
profit after tax, after depreciaiton = .69*(17000-16800) = 138
cash flow = 138+16800 = 16938
profit after tax, after depreciation for yr 2 = 0
cash flow for yr 2 = 17000
cash flow for yr 3 = 17000
cash flow for yr 4 = 17000*.69 = 11730
cash flow yr 4 = 11730+12000 = 23730
PV = (16938/1.11)+(17000/1.11^2)+(17000/1.11^3)+(11730/1.11^4)+(23730/1.11^5) = $63296.80
PV is less than Purchase price i.e 70,000
so he should not purchase it
4).
let machine price = x
Depreciation per year = x/5
let expected year = 6 years
cash flow per year till year 5 = (20000-x/5)*.67+x/5 = 13400+.33*x/5
cash flow in year 6 = 20000*.67 = $13400
PV = (13400+.33*x/5)*PVIFA(12,5)+(13400/1.12^6)
PV = (13400+.33*x/5)*3.6048+6788.857
PV = (13400+.33*x/5)*3.6048+6788.857 = 13400*3.6048+(.33*3.6048/5)*x+6788.857=48304.32+6788.857+.23791x = 55093.177+.23791x
let expected year = 7 years
cash flow per year till year 5 = (20000-x/5)*.67+x/5 = 13400+.33*x/5
cash flow in year 6 and 7 = 20000*.67 = $13400
PV = (13400+.33*x/5)*PVIFA(12,5)+(13400/1.12^6)+(13400/1.12^7)
PV = (13400+.33*x/5)*3.6048+6788.857 = 13400*3.6048+(.33*3.6048/5)*x+6788.857=48304.32+6788.857+.23791x = 55093.177+6061.479+.23791x = 61154.656+.23791x
let expected year = 8 years
cash flow per year till year 5 = (20000-x/5)*.67+x/5 = 13400+.33*x/5
cash flow in year 6 and 7 and 8 = 20000*.67 = $13400
PV = (13400+.33*x/5)*PVIFA(12,5)+(13400/1.12^6)+(13400/1.12^7)+(13400/1.12^8)
PV = (13400+.33*x/5)*3.6048+18262.37
PV = 13400*3.6048+.33*3.6048/5)*x+18262.37 = .2379x+48304.32+18262.37 = .2379x+66566.69
expected PV = .2*( 55093.177+.23791x)+.3*(61154.656+.23791x)+.5*(.23791x+66566.69)
expected PV = x
expected PV = .2*55093.177+.3*61154.656+.5*66566.69+.23791x
expected PV = 62648.377+.23791x
x = 62648.377+.23791x
.76209x = 62648.377
x = 62648.377/.76209 = 82206
it should pay $82206 for the machine