Time value of money problem help

[Devi09]

Hi, I need help with the second step of this problem: (please solve using financial calculator)

The Swell Computer Company has developed a new line of desktop computers. It is estimated that the cash returns generated by the new product line will be $800,000 per year for the next five years, and then $500,000 per year for 3 years after that (the cash returns occur at the end of each year). At a 9% interest rate, what is the present value of these cash returns?

So the 5yrs PV is: n=5 , i =9% PV=? FV= 0 PMT= 800,000 therefore PV= 3,111,721.01

The next 3 yrs however i don't know how to do. I thought it'd be the same process as the first step but it isn't. I've been told the answer is 822,575 but I don't know how to get there via the financial calculator.

Thanks

 

[DexterOnline]

Your number for present value of 3 payments in amount of $500,000 starting at the end of 6th year do not look correct

I get this amount as present value $822,583.93

You did not mention the amount for payments after the first 8 payments thus unable to get the net present value of the full investment

 

[Devi09]

Dexter may I ask how you got that PV number? As in your calculations?

Thanks

 

[DexterOnline]

Hi Devi09

Present value of deferred ordinary annuity


$\displaystyle PVA= 500,000 \times (1.09)^{-5} \times \frac{1-(1.09)^{-3}}{0.09}$
$\displaystyle PVA= 500,000 \times 0.64993138629834548405288188068363 \times \frac{1-0.77218348006106426960322896244022}{0.09}$
$\displaystyle PVA= 324965.69314917274202644094034182 \times \frac{0.22781651993893573039677103755978}{0.09}$
$\displaystyle PVA= 324965.69314917274202644094034182 \times 2.5312946659881747821863448617753$
$\displaystyle PVA= 822583.92569765091410066959622874$


Present value of deferred annuity due


$\displaystyle PVAD= 500,000 \times (1.09)^{-6} (1.09) \times \frac{1-(1.09)^{-3}}{0.09}$
$\displaystyle PVAD= 500,000 \times 0.59626732687921604041548796392994 (1.09) \times \frac{1-0.77218348006106426960322896244022}{0.09}$
$\displaystyle PVAD= 298133.66343960802020774398196497 \times (1.09) \times \frac{0.22781651993893573039677103755978}{0.09}$
$\displaystyle PVAD= 298133.66343960802020774398196497 \times 1.09 \times 2.5312946659881747821863448617753$
$\displaystyle PVAD= 298133.66343960802020774398196497 \times 2.7591111859271105125831158993351$
$\displaystyle PVAD= 822583.92569765091410066959622875$

 

[DexterOnline]

Hmmm.....error at last digit position?

Insignificant Digit

 

[DexterOnline]

Ah ha! You're now displaying insignificant digits

Sir Wilmer

I just recalculated the figures and it seems both amounts for PVA and PVAD match till the last insignificant digit of 4

So the odd insignificant digit of 5 in PVAD could have been a typo from my part

 

[DexterOnline]

A typo?! Go stand in the corner for 15 minutes (2 significant digits).

It's dark and cold at this corner

None of this fuss about significance or insignificance be around had I only showed the present value of ordinary annuity and annuity due to the nearest cent.

 

[DexterOnline]

Hi Devi09

$822,583.93 is the present value of 3 payments in amount of $500,000 starting at the end of year 6 discounted at 9% p.a.

Doesn't matter if you use ordinary annuity or an annuity due, the present value is same nevertheless