Lump-sum to annuity and Annuity to perpetuity

DexterOnline

DexterOnline

Junior Member
Joined
Jan 29, 2015
Messages
139
Given the interest rate is not used and is unknown, how would you find an equivalent annuity that costs the same as a lump-sum yet has the same yield (IRR).

Code: 
Lump sum

-10 0 0 0 0 0 0 0 0 0 15

Annuity
-10 ? ? ? ? ? ? ? ? ? ?

Further how would you find a perpetuity that costs the same as an annuity yet has the same yield (IRR).

Code: 
Annuity
-10 2 2 2 2 2 2 2 2 2 2

Perpetuity
-10 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ...
 
"Given the interest rate is not used and is unknown ..." What do you mean by that?
 
Ishuda said:
"Given the interest rate is not used and is unknown ..." What do you mean by that?
Click to expand...

It would be darn easy if we were allowed to use interest rate in determining the annuity amount or the perpetuity amount as all we would have to do is to solve for x

Annuity

Code: 
-10 + 15(1+i)^(-10) = -10 + x [1 - (1+i)^(-10)] / i

Perpetuity

Code: 
-10 + 2 [1 - (1+i)^(-10)] / i = -10 + x / i

where i is the IRR

But the real kick is to find x for annuity and for perpetuity when you are not allowed to make use of i
 
DexterOnline said:
It would be darn easy if we were allowed to use interest rate in determining the annuity amount or the perpetuity amount as all we would have to do is to solve for x

Annuity

Code: 
-10 + 15(1+i)^(-10) = -10 + x [1 - (1+i)^(-10)] / i

Perpetuity

Code: 
-10 + 2 [1 - (1+i)^(-10)] / i = -10 + x / i

where i is the IRR

But the real kick is to find x for annuity and for perpetuity when you are not allowed to make use of i
Click to expand...
Is this the type of thing you mean?

Annuity
Code: 
  x = 30 [(3/2)[SUP]1/10[/SUP] - 1] ~ $1.24
 
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