An APV example

A company is considering a project that wd cost $100,000 to be financed 50% by equity and 50% by debt. the financing method wd maintain the company’s WACC unchanged. Cashinflows will be 36000 pa in perpetuity, before interest charges. tax rate 30%. cost of equity 21.6, cost of debt 12% (before tax).

ok…. so the worked example does the calculations and i understand them. the NPVs using both the WACC and the APV give the same NPV.

next, he gives a twist and says now consider that the cashflows are only for 5 years and the tax is payable in arrears. in this new example he simply computes the tax shield, which i also understand.

on my own i am trying to calculate the NPVs using WACC and APV for the 5 year cash flow and i shd get the same answer right?

below is my working:

WACC = .5 x 21.6 + .5 x 12 X .3=15%
the cost of ordinary equity Ke=Ke1 + (1+T)(Ke1-ke)Vd/Ve).. and this gives the value for Ke1=17.64%

NPV using WACC of 15%:

cf————-0————-1————2———3——–4———–5—————6–
——-(1000000)—–36000—36000—36000–36000–36000——–
Tax——————————-(10800)–(10800)–(10800)–(10800)—–(10800)
Net–(100000)——36000–25200—25200—-25200—-25200—–(10800)
!5%—-1—————.87—–.756——-.658——-.572——-.497——-.432
PV—(100000)—–31320–19051—16582—-14414——12524—-(4666)

this give an NPV=100000-89225=(10775)

APV using 17.64%
APV: for the value of ungeared, Vu, i used the 17.64% and used the exact formula (1+r)^n

cf————-0————-1————2———3——–4———–5—————6–
Net–(100000)——36000–25200—25200—-25200—-25200—–(10800)
Df——–1—————.85—–.723——-.614——-.522——-.444——-.377

and i Get Vu=100000-84564=(15436)
to this i add the PV of tax benefits which is 9731
thus final NPV for the APVmethod is 5705

the 2 npvs are not equal.

where am i going wrong

thank u