Project Appraisal

On page 37 of CT1 Chapter 10 (solution for an exam-style question):

It states:

For Project B, the discounted payback period must be a whole number of 6 years, since cashflows only occur at annual intervals. We need to find the smallest integer value of n of which:

-0.1(A due 10) + 0.045v^10(Ia[n]) > 0

My question is, shouldn't the equation be equal/larger than zero, rather than just larger than zero?

Thanks in advance for your help!

 

hi friend, it should be just greater than zero.
why because

if you take greater than or equal to zero it means you are taking fraction of years also into consideration.

where as if take greater than zero you are ignoring fraction of years.

for Eg: the calculation may give 5 years 2 months 3 days as pay back period
but in real situation the payment may be made at the end of 6th year.....
in this case we consider 6 years as pay back period.

 

Would it make a difference to the solution if it were >=?

 

If you take >= zero, The equation solution would be same
like below
\(\require{enclose}\ {Ia}_{\enclose{actuarial}{n}}\) >= 32.852

which means
\(\require{enclose}\ {Ia}_{\enclose{actuarial}{n}}\) = 32.852

OR \(\require{enclose}\ {Ia}_{\enclose{actuarial}{n}}\) > 32.852

* But to find n value for equal-to equation we need to interpolate between
at 9years =29.656 & 10years =34.739 which means "n=9.629"

this means the payback period would be 19.629 years.

Since in the project B, there are no continuous cash flows, we are not allowed to take this as payback period.

even though if you consider this is as payback period &
calculate accumulated value of cash flows after this period.
you may get some answer. but conceptually it may not correct.

(i.e. in the question it is straight away given the cash outflow are made at the start of each year, for income the payment begins at time 11 which is also means start of year) .

if there is any thing else please quote.

 

Hi all,
Answer will be same....... Whether > or >=
19.629 is absolutely wrong answer. And the way of solving is not what math says.
Answer for n will be 10 only.

 

Hi friend.........!
in this problem, if you write

-0.1\(\require{enclose}\ddot {a}_{\enclose{actuarial}{10}}\)+0.045 \(v^{10}\)\(\require{enclose}\ {(Ia)}_{\enclose{actuarial}{n}}\)>=0

means this two equations.

-0.1\(\require{enclose}\ddot {a}_{\enclose{actuarial}{10}}\)+0.045 \(v^{10}\)\(\require{enclose}\ {(Ia)}_{\enclose{actuarial}{n}}\)=0

(OR)

-0.1\(\require{enclose}\ddot {a}_{\enclose{actuarial}{10}}\)+0.045 \(v^{10}\)\(\require{enclose}\ {(Ia)}_{\enclose{actuarial}{n}}\)>0

could you please solve this equal-to equation for me (if you solve this by trail and error you will come to know why n=9.629...)

If you say, we need to ignore this what is the meaning in writing and ignoring........!

 

Actually friend it does't matter if n is not an integer , as we know for this problem ='s equality won't give n as integer.
All we need is to find the minimum n that has nonnegative cash. Every cash flow happens annually, so the answer is 10 whether take >='s or >'s way.
Previously you took 10+9.6 but we need 9.6 or 10 ....although 9.6 is minimum but it is not valid ,so and is 10

 

that is what i am saying.....

integer or not will becomes matter only when there are continuous cash flows in the problem......

since in this problem there are no continuous cash flows no need to worry about equal to.

please read my post (#4) carefully there is one line.

(Since in the project B, there are no continuous cash flows, we are not allowed to take this as payback period.)

 

Now you're right!

Before you said,"this means the payback period would be 19.629 years."

 

that means, he asked a question so answered , what would have happened.