Question

Your company is deciding whether to invest in a new machine. The new machine will increase cash flow by $318,000 per year. You believe the technology used in the machine has a 10-year life; in other words, no matter when you purchase the machine, it will be obsolete 10 years from today. The machine is currently priced at $1,710,000. The cost of the machine will decline by $105,000 per year until it reaches $1,185,000, where it will remain.

  

If your required return is 13 percent, calculate the NPV today. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

NPV

$

   

If your required return is 13 percent, calculate the NPV if you wait to purchase the machine until the indicated year. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

  

	NPV
Year 1	$
Year 2	$
Year 3	$
Year 4	$
Year 5	$
Year 6	$

   

Should you purchase the machine?

Yes No

  

If so, when should you purchase it?

Today One year from now Two years from now

This is all the information I was provided with for this question. There was nothing more provided.

Answer 1

If Machine is purchase today

We will receive 10 cash inflows equally starting from year 1 and one terminal inflow at the end of the 10^th year

r=13% or 0.13 n= 10 years

Formula for equal cashflow

=CF­₀ +CF x 1-(1/(1+r)ⁿ/r+ CF₁₀ x 1/(1+r)¹⁰

= [-$1,710,000]+[$318,000 x 1-(1/(1+0.13)¹⁰/0.13]+[$1,185,000x 1/(1+0.13)¹⁰]

= [-$1,710,000]+[$318,000 x 1-(1/(1.13)¹⁰/0.13]+$1,185,000 x 1/(1.13)¹⁰

=[-$1,710,000+ $318,000] x[ 1-(1/3.39456739/0.13]+[$1,185,000 x 0.294588348]

= [-$1,710,000]+[$318,000 x (1-0.294588348)/0.13]+$349,087.19

=[ -$1,710,000]+[$318,000 x 0.705411652/0.13]+[$349,087.19]

= [-$1,710,000]+[$318,000 x5.426243476]+[$349,087.19]

=[-$1,710,000]+ [1,725,545.425]+[$349,087.19]

NPV=$364,632.62

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If Machine is purchased one year from now

We will receive 9 cash inflows equally starting from year 2 and one terminal inflow at the end of the 10^th year

r=13% or 0.13 n= 9 years t= cashflow starts from year 2

Formula for equal cashflow

=[CF­₀ x 1/(1+r)¹] +[CF x 1-(1/(1+r)ⁿ/r] x 1/(1+r)^t+ [CF₁₀ x 1/(1+r)¹⁰]

= [$1,710,000 x(1/1+0.13)¹] +{[$318,000 x 1-(1/(1+0.13)⁹/0.13]x 1/(1+0.13)¹}+[$1,185,000x 1/(1+0.13)¹⁰]

= [-$1,710,000 x 1/1.13]+ {[$318,000 x 1-(1/(1+0.13)⁹/0.13]x 1/(1+0.13)¹}+$1,185,000 x 1/(1.13)¹⁰

=[-$1,710,000 x 0.8849+ {[$318,000 x 1-(1/(1+0.13)⁹/0.13]x 1/(1.13)}+[$1,185,000 x 0.294588348]

= [-$15,13,274.34]+ {[$318,000 x 1-(1/3.004041938/0.13]x 0.884955752}+$349,087.19

=[ -$15,13,274.34]+ {[$318,000 x 1-(0.332884833/0.13]x 0.884955752}+[$349,087.19]

= [-$15,13,274.34]+ {[$318,000 x 0.667115167/0.13]x 0.884955752}+[$349,087.19]

=[-$15,13,274.34]+ {[$318,000 x 5.131655128 x 0.884955752}+[$349,087.19]

=[-$15,13,274.34]+ {[$318,000 x4.541287724}+[$349,087.19]

=[-$15,13,274.34]+[ $14,44,129.50 ]+[$349,087.19]

NPV= $2,79,942.35

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If Machine is purchased 2 years from now

We will receive 8 cash inflows equally starting from year 3 and one terminal inflow at the end of the 10^th year

r=13% or 0.13 n= 8 years t= cashflow starts from year 3

Formula for equal cashflow

=[CF­₀ x 1/(1+r)²] +[CF x 1-(1/(1+r)ⁿ/r] x 1/(1+r)^t+ [CF₁₀ x 1/(1+r)¹⁰]

= [$1,710,000 x(1/1+0.13)²] +{[$318,000 x 1-(1/(1+0.13)⁸/0.13]x 1/(1+0.13)²}+[$1,185,000x 1/(1+0.13)¹⁰]

= [-$1,710,000 x 1/1.13²]+ {[$318,000 x 1-(1/(1+0.13)⁸/0.13]x 1/(1+0.13)²}+$1,185,000 x 1/(1.13)¹⁰

=[-$1,710,000 x 0.783146683+ {[$318,000 x 1-(1/(1+0.13)⁸/0.13]x 1/(1.13)}+[$1,185,000 x 0.294588348]

= [-$13,39,180.83]+ {[$318,000 x 1-(1/ 2.658444193/0.13]x 0.783146683}+$349,087.19

=[-$13,39,180.83]+ {[$318,000 x 1-( 0.376159862/0.13]x 0.783146683}+[$349,087.19]

= [-$13,39,180.83]+ {[$318,000 x 0.623840138/0.13]x 0.783146683}+[$349,087.19]

=[-$13,39,180.83]+ {[$318,000 x 4.798770294 x 0.783146683}+[$349,087.19]

=[-$13,39,180.83]+ {[$318,000 x 3.75814104}+[$349,087.19]

=[-$13,39,180.83]+[ $11,95,088.85 ]+[$349,087.19]

NPV= $2,04,995.21

If Machine is purchased 3 years from now

We will receive 7 cash inflows equally starting from year 4 and one terminal inflow at the end of the 10^th year

r=13% or 0.13 n= 7 years t= cashflow starts from year 4

Formula for equal cashflow

=[CF­₀ x 1/(1+r)³] +[CF x 1-(1/(1+r)ⁿ/r] x 1/(1+r)^t+ [CF₁₀ x 1/(1+r)¹⁰]

= [$1,710,000 x(1/1+0.13)³] +{[$318,000 x 1-(1/(1+0.13)⁷/0.13]x 1/(1+0.13)³}+[$1,185,000x 1/(1+0.13)¹⁰]

= [-$1,710,000 x 1/1.13³]+ {[$318,000 x 1-(1/(1+0.13)⁷/0.13]x 1/(1+0.13)³}+$1,185,000 x 1/(1.13)¹⁰

=[-$1,710,000 x 0.693050162+ {[$318,000 x 1-(1/(1+0.13)⁷/0.13]x 1/(1.13)}+[$1,185,000 x 0.294588348]

= [-$11,85,115.78]+ {[$318,000 x 1-(1/ 2.35260548/0.13]x 0.693050162}+$349,087.19

=[-$11,85,115.78]+ {[$318,000 x 1-( 0.425060644/0.13]x 0.693050162}+[$349,087.19]

= [-$11,85,115.78]+ {[$318,000 x0.574939356/0.13]x 0.693050162}+[$349,087.19]

=[-$11,85,115.78]+ {[$318,000 x 4.422610433 x 0.693050162}+[$349,087.19]

=[-$11,85,115.78]+ {[$318,000 x 3.065090878}+[$349,087.19]

=[-$11,85,115.78]+[ $9,74,698.90 ]+[$349,087.19]

NPV= $ $1,38,670.31

If Machine is purchased 4 years from now

We will receive 6 cash inflows equally starting from year 5 and one terminal inflow at the end of the 10^th year

r=13% or 0.13 n= 6 years t= cashflow starts from year 5

Formula for equal cashflow

=[CF­₀ x 1/(1+r)⁴] +[CF x 1-(1/(1+r)ⁿ/r] x 1/(1+r)^t+ [CF₁₀ x 1/(1+r)¹⁰]

= [$1,710,000 x(1/1+0.13)⁴] +{[$318,000 x 1-(1/(1+0.13)⁶/0.13]x 1/(1+0.13)⁴}+[$1,185,000x 1/(1+0.13)¹⁰]

= [-$1,710,000 x 1/1.13⁴]+ {[$318,000 x 1-(1/(1+0.13)⁶/0.13]x 1/(1+0.13)⁴}+$1,185,000 x 1/(1.13)¹⁰

=[-$1,710,000 x 0.613318728+ {[$318,000 x 1-(1/(1+0.13)⁶/0.13]x 1/(1.13)}+[$1,185,000 x 0.294588348]

= [-$11,85,115.78]+ {[$318,000 x 1-(1/ 2.081951753/0.13]x 0.613318728}+$349,087.19

=[-$11,85,115.78]+ {[$318,000 x 1-( 0.480318527/0.13]x 0.613318728}+[$349,087.19]

= [-$11,85,115.78]+ {[$318,000 x 0.519681473/0.13]x 0.613318728}+[$349,087.19]

=[-$11,85,115.78]+ {[$318,000 x 3.997549789 x 0.613318728}+[$349,087.19]

=[-$11,85,115.78]+ {[$318,000 x 2.45177215}+[$349,087.19]

=[-$11,85,115.78]+[ $7,79,663.54   ]+[$349,087.19]

NPV= $ 79,975.71

If Machine is purchased 5 years from now

We will receive 5 cash inflows equally starting from year 6 and one terminal inflow at the end of the 10^th year

r=13% or 0.13 n= 5 years t= cashflow starts from year 6

Formula for equal cashflow

=[CF­₀ x 1/(1+r)⁵] +[CF x 1-(1/(1+r)ⁿ/r] x 1/(1+r)^t+ [CF₁₀ x 1/(1+r)¹⁰]

= [$1,710,000 x(1/1+0.13)⁵] +{[$318,000 x 1-(1/(1+0.13)⁵/0.13]x 1/(1+0.13)⁵}+[$1,185,000x 1/(1+0.13)¹⁰]

= [-$1,710,000 x 1/1.13⁵]+ {[$318,000 x 1-(1/(1+0.13)⁵/0.13]x 1/(1+0.13)⁵}+$1,185,000 x 1/(1.13)¹⁰

=[-$1,710,000 x 0.542759936+ {[$318,000 x 1-(1/(1+0.13)⁵/0.13]x 1/(1.13)}+[$1,185,000 x 0.294588348]

= [-$9,28,119.49]+ {[$318,000 x 1-(1/1.842435179/0.13]x 0.542759936}+$349,087.19

=[-$9,28,119.49]+ {[$318,000 x 1-( 0.542759936/0.13]x 0.542759936}+[$349,087.19]

= [-$9,28,119.49]+ {[$318,000 x 0.457240064/0.13]x 0.542759936}+[$349,087.19]

=[-$9,28,119.49]+ {[$318,000 x 3.517231262 x 0.542759936}+[$349,087.19]

=[-$9,28,119.49]+ {[$318,000 x 1.909012214}+[$349,087.19]

=[-$9,28,119.49]+[ $6,07,065.88 ]+[$349,087.19]

NPV= $28,033.59

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If Machine is purchased 6 years from now

We will receive 4 cash inflows equally starting from year 7 and one terminal inflow at the end of the 10^th year

r=13% or 0.13 n= 7 years t= cashflow starts from year 7

Formula for equal cashflow

=[CF­₀ x 1/(1+r)⁵] +[CF x 1-(1/(1+r)ⁿ/r] x 1/(1+r)^t+ [CF₁₀ x 1/(1+r)¹⁰]

= [$1,710,000 x(1/1+0.13)⁶] +{[$318,000 x 1-(1/(1+0.13)⁴/0.13]x 1/(1+0.13)⁶}+[$1,185,000x 1/(1+0.13)¹⁰]

= [-$1,710,000 x 1/1.13⁶]+ {[$318,000 x 1-(1/(1+0.13)⁴/0.13]x 1/(1+0.13)⁶}+$1,185,000 x 1/(1.13)¹⁰

=[-$1,710,000 x 0.480318527+ {[$318,000 x 1-(1/(1+0.13)⁴/0.13]x 1/(1.13)}+[$1,185,000 x 0.294588348]

= [-$8,21,344.68]+ {[$318,000 x 1-(1/ 1.63047361/0.13]x 0.480318527}+$349,087.19

=[-$8,21,344.68]+ {[$318,000 x 1-( 0.613318728/0.13]x 0.480318527}+[$349,087.19]

= [-$8,21,344.68]+ {[$318,000 x 0.386681272/0.13]x 0.480318527}+[$349,087.19]

=[-$8,21,344.68]+ {[$318,000 x 2.974471326 x 0.480318527}+[$349,087.19]

=[-$8,21,344.68]+ {[$318,000 x 1.428693687}+[$349,087.19]

=[-$8,21,344.68]+[ $ $4,54,324.59 ]+[$349,087.19]

NPV= $17,932.90

Year	NPV
year1	$2,79,942.35
year2	$2,04,995.21
year3	$1,38,670.31
year4	$79,975.71
year5	$28,033.59
year6	$(17,932.90)

Yes We should buy Machine as ther is positive NPV

We should buy today as NPV is higher I.e $3,64,632.62