Answer:
b. NPW(SL): $33,738; NPW(DDB): $37,068; Recommendation: DDB
Explanation:
The computation is shown below:
As we know that 
Present value is 
=  [Cash Flow ÷ (1 + Rate of Interest)^Year]
where, 
Rate of Interest = 10%
Under Straight-line depreciation:
Beginning book value = $50,000
Salvage value = $5,500
So, the depreciationper year is
=  [($50,000 - $5,500) ÷ 5] 
= $8,900
<u>Year    Beginning   Depreciation  End                 Present value </u>
<u>            book value                  book value	of depreciation
</u>
1            $50,000      $8,900        $41,100             $8,090.91
2           $41,100         $8,900        $32,200           $7,355.37
3           $32,200       $8,900         $23,300           $6,686.70
4           $23,300       $8,900         $14,400           $6,078.82
5           $14,400        $8,900         $5,500              $5,526.20
                                                                                   $33,738.00
Under Double declining depreciation:
Depreciation rate per year = (1 ÷ Useful  Life) × 100 
= 1 ÷ 5 × 100
= 20%
Now for double-declining, the rate is doubled 
So, 
= 20% × 2
= 40%
<u>Year    Beginning   Depreciation  End                 Present value </u>
<u>            book value                  book value	of depreciation
</u>
1            $50,000      $20,000       $30,000           $18,181.82
2           $30,000       $12,000       $18,000            $9,917.36
3           $18,000       $7,200         $10,800            $5,409.47
4           $10,800       $4,320         $6,480             $2,950.62
5           $6,480       $980              $5,500            $608.50
                                                                                 $37,068