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